[{"date_updated":"2025-05-19T13:52:10Z","abstract":[{"lang":"eng","text":"Given a fixed finite metric space (V,μ), the {\\em minimum 0-extension problem}, denoted as 0-Ext[μ], is equivalent to the following optimization problem: minimize function of the form minx∈Vn∑ifi(xi)+∑ijcijμ(xi,xj) where cij,cvi are given nonnegative costs and fi:V→R are functions given by fi(xi)=∑v∈Vcviμ(xi,v). The computational complexity of 0-Ext[μ] has been recently established by Karzanov and by Hirai: if metric μ is {\\em orientable modular} then 0-Ext[μ] can be solved in polynomial time, otherwise 0-Ext[μ] is NP-hard. To prove the tractability part, Hirai developed a theory of discrete convex functions on orientable modular graphs generalizing several known classes of functions in discrete convex analysis, such as L♮-convex functions. We consider a more general version of the problem in which unary functions fi(xi) can additionally have terms of the form cuv;iμ(xi,{u,v}) for {u,v}∈F, where set F⊆(V2) is fixed. We extend the complexity classification above by providing an explicit condition on (μ,F) for the problem to be tractable. In order to prove the tractability part, we generalize Hirai's theory and define a larger class of discrete convex functions. It covers, in particular, another well-known class of functions, namely submodular functions on an integer lattice. Finally, we improve the complexity of Hirai's algorithm for solving 0-Ext on orientable modular graphs.\r\n"}],"title":"Generalized minimum 0-extension problem and discrete convexity","author":[{"orcid":"0000-0001-5293-214X","first_name":"Martin","last_name":"Dvorak","id":"40ED02A8-C8B4-11E9-A9C0-453BE6697425","full_name":"Dvorak, Martin"},{"full_name":"Kolmogorov, Vladimir","id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","first_name":"Vladimir","last_name":"Kolmogorov"}],"external_id":{"arxiv":["2109.10203"],"isi":["001176563300001"]},"date_created":"2021-09-27T10:48:23Z","date_published":"2025-01-01T00:00:00Z","OA_type":"hybrid","corr_author":"1","publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file_date_updated":"2025-04-16T09:36:08Z","publication":"Mathematical Programming","publisher":"Springer Nature","citation":{"ieee":"M. Dvorak and V. Kolmogorov, “Generalized minimum 0-extension problem and discrete convexity,” <i>Mathematical Programming</i>, vol. 209. Springer Nature, pp. 279–322, 2025.","mla":"Dvorak, Martin, and Vladimir Kolmogorov. “Generalized Minimum 0-Extension Problem and Discrete Convexity.” <i>Mathematical Programming</i>, vol. 209, Springer Nature, 2025, pp. 279–322, doi:<a href=\"https://doi.org/10.1007/s10107-024-02064-5\">10.1007/s10107-024-02064-5</a>.","short":"M. Dvorak, V. Kolmogorov, Mathematical Programming 209 (2025) 279–322.","ista":"Dvorak M, Kolmogorov V. 2025. Generalized minimum 0-extension problem and discrete convexity. Mathematical Programming. 209, 279–322.","chicago":"Dvorak, Martin, and Vladimir Kolmogorov. “Generalized Minimum 0-Extension Problem and Discrete Convexity.” <i>Mathematical Programming</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s10107-024-02064-5\">https://doi.org/10.1007/s10107-024-02064-5</a>.","apa":"Dvorak, M., &#38; Kolmogorov, V. (2025). Generalized minimum 0-extension problem and discrete convexity. <i>Mathematical Programming</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10107-024-02064-5\">https://doi.org/10.1007/s10107-024-02064-5</a>","ama":"Dvorak M, Kolmogorov V. Generalized minimum 0-extension problem and discrete convexity. <i>Mathematical Programming</i>. 2025;209:279-322. doi:<a href=\"https://doi.org/10.1007/s10107-024-02064-5\">10.1007/s10107-024-02064-5</a>"},"quality_controlled":"1","ddc":["004"],"day":"01","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","_id":"10045","article_type":"original","scopus_import":"1","department":[{"_id":"GradSch"},{"_id":"VlKo"}],"intvolume":"       209","arxiv":1,"isi":1,"month":"01","has_accepted_license":"1","page":"279-322","doi":"10.1007/s10107-024-02064-5","oa":1,"year":"2025","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"file":[{"file_id":"19578","success":1,"creator":"dernst","access_level":"open_access","relation":"main_file","date_created":"2025-04-16T09:36:08Z","content_type":"application/pdf","file_size":839510,"checksum":"25d9bd490719b45eca84f4d93a06c69f","file_name":"2025_MathProgramming_Dvorak.pdf","date_updated":"2025-04-16T09:36:08Z"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0025-5610"],"eissn":["1436-4646"]},"status":"public","OA_place":"publisher","volume":209,"keyword":["minimum 0-extension problem","metric labeling problem","discrete metric spaces","metric extensions","computational complexity","valued constraint satisfaction problems","discrete convex analysis","L-convex functions"],"type":"journal_article","acknowledgement":"We thank the anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions. Open access funding provided by Institute of Science and Technology (IST Austria)."},{"citation":{"ama":"Draganov O. Structures and computations in topological data analysis. 2025. doi:<a href=\"https://doi.org/10.15479/at:ista:18979\">10.15479/at:ista:18979</a>","apa":"Draganov, O. (2025). <i>Structures and computations in topological data analysis</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:18979\">https://doi.org/10.15479/at:ista:18979</a>","chicago":"Draganov, Ondrej. “Structures and Computations in Topological Data Analysis.” Institute of Science and Technology Austria, 2025. <a href=\"https://doi.org/10.15479/at:ista:18979\">https://doi.org/10.15479/at:ista:18979</a>.","ista":"Draganov O. 2025. Structures and computations in topological data analysis. Institute of Science and Technology Austria.","short":"O. Draganov, Structures and Computations in Topological Data Analysis, Institute of Science and Technology Austria, 2025.","mla":"Draganov, Ondrej. <i>Structures and Computations in Topological Data Analysis</i>. Institute of Science and Technology Austria, 2025, doi:<a href=\"https://doi.org/10.15479/at:ista:18979\">10.15479/at:ista:18979</a>.","ieee":"O. Draganov, “Structures and computations in topological data analysis,” Institute of Science and Technology Austria, 2025."},"supervisor":[{"orcid":"0000-0002-9823-6833","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","full_name":"Edelsbrunner, Herbert"}],"ddc":["514","004"],"publisher":"Institute of Science and Technology Austria","alternative_title":["ISTA Thesis"],"department":[{"_id":"GradSch"},{"_id":"HeEd"}],"day":"03","_id":"18979","oa_version":"Published Version","article_processing_charge":"No","project":[{"_id":"2561EBF4-B435-11E9-9278-68D0E5697425","grant_number":"I02979-N35","name":"Persistence and stability of geometric complexes","call_identifier":"FWF"},{"call_identifier":"FWF","grant_number":"Z00342","name":"Mathematics, Computer Science","_id":"268116B8-B435-11E9-9278-68D0E5697425"}],"date_created":"2025-01-31T17:04:40Z","title":"Structures and computations in topological data analysis","author":[{"id":"2B23F01E-F248-11E8-B48F-1D18A9856A87","full_name":"Draganov, Ondrej","first_name":"Ondrej","last_name":"Draganov","orcid":"0000-0003-0464-3823"}],"date_updated":"2026-04-07T11:47:30Z","abstract":[{"text":"Topological Data Analysis (TDA) is a discipline utilizing the mathematical field of topology to study data, most prominently collections of point sets. This thesis summarizes three projects related to computations in TDA.\r\n\r\nThe first one establishes a variant of TDA for chromatic point sets, where each point is given a color. For example, we are given positions of cells within a tumor microenvironment, and color the cancerous cells red, and the immune cells blue.\r\n\r\nThe aim is then to give a quantitative description of how the two or more sets of points spatially interact. Building on image, kernel and cokernel variants of persistent homology, we suggest six-packs of persistent diagrams as such a descriptor.\r\n\r\nWe describe a construction of a chromatic alpha complex, which enables  efficient computation of several variants of the six-packs. We give topological descriptions of natural subcomplexes of the chromatic alpha complex, and show that the radii of the simplices form a discrete Morse function. Finally, we provide an implementation of the presented chromatic TDA pipeline.\r\n\r\nThe second part aims to translate a powerful tool of sheaf theory to elementary terms using labeled matrices. The goal is to enable their use in computational settings. We show that derived categories of sheaves over finite posets have, up to isomorphism, unique objects---minimal injective resolutions---and give a concrete algorithm to compute them. We further describe simple algorithms to compute derived pushforwards and pullbacks for monotonic maps, and their proper variants for inclusions, and demonstrate their tractability by providing an implementation. Finally, we suggest a discrete definition of microsupport and show desirable properties inspired by discrete Morse theory.\r\n\r\nIn the last part, we present a collection of observations about collapses. We give a characterization of collapsibility in terms of unitriangular submatrices of the boundary matrix, a cotree-tree decomposition, and the optimal solution to a variant of the Procrustes problem. We establish relation between dual collapses and relative Morse theory and pose several open questions. Finally, focusing on complexes embedded in the three-dimensional Euclidean space, we describe a relation between the collapsibility and the triviality of a polygonal knot.","lang":"eng"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","publication_status":"published","file_date_updated":"2025-02-04T16:22:07Z","date_published":"2025-02-03T00:00:00Z","corr_author":"1","OA_place":"publisher","keyword":["topological data analysis","chromatic point set","alpha complex","persistent homology","six pack","sheaf","microlocal discrete Morse","injective resolution","collapse","knot","discrete Morse theory"],"publication_identifier":{"issn":["2663-337X"]},"status":"public","acknowledgement":"The research presented in this thesis was funded with the Wittgenstein Prize,\r\nAustrian Science Fund (FWF), grant no. Z 342-N31, and from the DFG Collaborative Research\r\nCenter TRR 109, ‘Discretization in Geometry and Dynamics’, Austrian Science Fund (FWF),\r\ngrant no. I 02979-N35.\r\n","type":"dissertation","degree_awarded":"PhD","month":"02","year":"2025","oa":1,"language":[{"iso":"eng"}],"file":[{"content_type":"application/zip","file_size":11899491,"checksum":"af6567e5d35e5eb330b8925ae37f1998","file_name":"Thesis.zip","date_updated":"2025-01-31T16:58:30Z","relation":"source_file","date_created":"2025-01-31T16:58:30Z","creator":"odragano","access_level":"closed","file_id":"18983"},{"relation":"main_file","date_created":"2025-02-04T16:22:07Z","file_size":8857514,"content_type":"application/pdf","checksum":"c3fef68e35b9dc2020b2ca6006da6343","file_name":"Thesis.pdf","date_updated":"2025-02-04T16:22:07Z","file_id":"19000","creator":"odragano","access_level":"open_access"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"doi":"10.15479/at:ista:18979","has_accepted_license":"1","page":"140","related_material":{"record":[{"relation":"part_of_dissertation","id":"15091","status":"public"},{"relation":"part_of_dissertation","id":"18981","status":"public"}]}},{"publication_status":"published","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","file_date_updated":"2024-12-19T10:24:50Z","date_published":"2024-12-17T00:00:00Z","corr_author":"1","project":[{"_id":"266A2E9E-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Alpha Shape Theory Extended","grant_number":"788183"}],"title":"New methods for applying topological data analysis to materials science","author":[{"full_name":"Heiss, Teresa","id":"4879BB4E-F248-11E8-B48F-1D18A9856A87","last_name":"Heiss","first_name":"Teresa","orcid":"0000-0002-1780-2689"}],"date_created":"2024-12-17T16:17:55Z","date_updated":"2026-04-07T12:54:10Z","abstract":[{"lang":"eng","text":"Many chemical and physical properties of materials are determined by the material’s shape,\r\nfor example the size of its pores and the width of its tunnels. This makes materials science\r\na prime application area for geometrical and topological methods. Nevertheless many\r\nmethods in topological data analysis have not been satisfyingly extended to the needs of\r\nmaterials science. This thesis provides new methods and new mathematical theorems\r\ntargeted at those specific needs by answering four different research questions. While the\r\nmotivation for each of the research questions arises from materials science, the methods\r\nare versatile and can be applied in different areas as well. \r\n\r\nThe first research question is concerned with image data, for example a three-dimensional\r\ncomputed tomography (CT) scan of a material, like sand or stone. There are two commonly\r\nused topologies for digital images and depending on the application either of them might be\r\nrequired. However, software for computing the topological data analysis method persistence\r\nhomology, usually supports only one of the two topologies. We answer the question how to\r\ncompute persistent homology of an image with respect to one of the two topologies using\r\nsoftware that is intended for the other topology. \r\n\r\nThe second research question is concerned with image data as well, and asks how much\r\nof the topological information of an image is lost when the resolution is coarsened. As\r\ncomputer tomography scanners are more expensive the higher the resolution, it is an\r\nimportant question in materials science to know which resolution is enough to get satisfying\r\npersistent homology. We give theoretical bounds on the information loss based on different\r\ngeometrical properties of the object to be scanned. In addition, we conduct experiments on\r\nsand and stone CT image data. \r\n\r\nThe third research question is motivated by comparing crystalline materials efficiently. As\r\nthe atoms within a crystal repeat periodically, crystalline materials are either modeled by\r\nunmanageable infinite periodic point sets, or by one of their fundamental domains, which is\r\nunstable under perturbation. Therefore a fingerprint of crystalline materials is needed, with\r\nappropriate properties such that comparing the crystals can be eased by comparing the\r\nfingerprints instead. We define the density fingerprint and prove the necessary properties. \r\n\r\nThe fourth research question is motivated by studying the hole-structure or connectedness,\r\ni.e. persistent homology or merge trees, of crystalline materials. A common way to deal\r\nwith periodicity is to take a fundamental domain and identify opposite boundaries to form a\r\ntorus. However, computing persistent homology or merge trees on that torus loses some\r\nof the information materials scientists are interested in and is additionally not stable under\r\ncertain noise. We therefore decorate the merge tree stemming from the torus with additional\r\ninformation describing the density and growth rate of the periodic copies of a component\r\nwithin a growing spherical window. We prove all desired properties, like stability and efficient\r\ncomputability."}],"department":[{"_id":"GradSch"},{"_id":"HeEd"}],"alternative_title":["ISTA Thesis"],"day":"17","article_processing_charge":"No","oa_version":"Published Version","_id":"18667","supervisor":[{"orcid":"0000-0002-9823-6833","last_name":"Edelsbrunner","first_name":"Herbert","full_name":"Edelsbrunner, Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87"}],"citation":{"ama":"Heiss T. New methods for applying topological data analysis to materials science. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:18667\">10.15479/at:ista:18667</a>","apa":"Heiss, T. (2024). <i>New methods for applying topological data analysis to materials science</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:18667\">https://doi.org/10.15479/at:ista:18667</a>","chicago":"Heiss, Teresa. “New Methods for Applying Topological Data Analysis to Materials Science.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:18667\">https://doi.org/10.15479/at:ista:18667</a>.","ista":"Heiss T. 2024. New methods for applying topological data analysis to materials science. Institute of Science and Technology Austria.","ieee":"T. Heiss, “New methods for applying topological data analysis to materials science,” Institute of Science and Technology Austria, 2024.","mla":"Heiss, Teresa. <i>New Methods for Applying Topological Data Analysis to Materials Science</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:18667\">10.15479/at:ista:18667</a>.","short":"T. Heiss, New Methods for Applying Topological Data Analysis to Materials Science, Institute of Science and Technology Austria, 2024."},"ddc":["514","516","004"],"publisher":"Institute of Science and Technology Austria","oa":1,"year":"2024","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"file":[{"date_created":"2024-12-19T10:24:46Z","relation":"main_file","content_type":"application/pdf","file_size":7752253,"checksum":"247bb057aed2fba1cd4711917aaa2d77","date_updated":"2024-12-19T10:24:46Z","file_name":"Teresa_Heiss_PhD_Thesis_final.pdf","file_id":"18686","access_level":"open_access","success":1,"creator":"theiss"},{"file_id":"18687","access_level":"closed","creator":"theiss","date_created":"2024-12-19T10:24:50Z","relation":"source_file","content_type":"application/zip","checksum":"9648b45c07a008ee11a07f99856a139d","file_size":17197731,"date_updated":"2024-12-19T10:24:50Z","file_name":"PhD_Thesis.zip"}],"language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"10828"},{"id":"11440","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"18673","status":"public"},{"status":"public","id":"9345","relation":"part_of_dissertation"}]},"page":"111","has_accepted_license":"1","doi":"10.15479/at:ista:18667","month":"12","acknowledgement":"I was supported by the European Research Council (ERC) Horizon 2020 project\r\n“Alpha Shape Theory Extended” No. 788183 and by the Pöttinger Scholarship. In addition,\r\nI am very thankful for having been able to attend the second Workshop for Women in\r\nComputational Topology in July 2019, funded by the Mathematical Sciences Institute at\r\nANU, the US National Science Foundation through the award CCF-1841455, the Australian\r\nMathematical Sciences Institute and the Association for Women in Mathematics. Two of the\r\nprojects presented in this thesis started there. One of them reached completion thanks to\r\nfunding from the MSRI Summer Research in Mathematics program awarded to me and my\r\ncollaborators in 2020.","degree_awarded":"PhD","type":"dissertation","OA_place":"publisher","keyword":["persistent homology","topological data analysis","periodic","crystalline materials","images","fingerprint"],"publication_identifier":{"issn":["2663-337X"],"isbn":["978-3-99078-052-7"]},"ec_funded":1,"status":"public"},{"ddc":["510"],"quality_controlled":"1","citation":{"ista":"Kwan MA, Sah A, Sauermann L, Sawhney M. 2023. Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture. Forum of Mathematics, Pi. 11, e21.","mla":"Kwan, Matthew Alan, et al. “Anticoncentration in Ramsey Graphs and a Proof of the Erdős–McKay Conjecture.” <i>Forum of Mathematics, Pi</i>, vol. 11, e21, Cambridge University Press, 2023, doi:<a href=\"https://doi.org/10.1017/fmp.2023.17\">10.1017/fmp.2023.17</a>.","short":"M.A. Kwan, A. Sah, L. Sauermann, M. Sawhney, Forum of Mathematics, Pi 11 (2023).","ieee":"M. A. Kwan, A. Sah, L. Sauermann, and M. Sawhney, “Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture,” <i>Forum of Mathematics, Pi</i>, vol. 11. Cambridge University Press, 2023.","apa":"Kwan, M. A., Sah, A., Sauermann, L., &#38; Sawhney, M. (2023). Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture. <i>Forum of Mathematics, Pi</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fmp.2023.17\">https://doi.org/10.1017/fmp.2023.17</a>","ama":"Kwan MA, Sah A, Sauermann L, Sawhney M. Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture. <i>Forum of Mathematics, Pi</i>. 2023;11. doi:<a href=\"https://doi.org/10.1017/fmp.2023.17\">10.1017/fmp.2023.17</a>","chicago":"Kwan, Matthew Alan, Ashwin Sah, Lisa Sauermann, and Mehtaab Sawhney. “Anticoncentration in Ramsey Graphs and a Proof of the Erdős–McKay Conjecture.” <i>Forum of Mathematics, Pi</i>. Cambridge University Press, 2023. <a href=\"https://doi.org/10.1017/fmp.2023.17\">https://doi.org/10.1017/fmp.2023.17</a>."},"publisher":"Cambridge University Press","intvolume":"        11","department":[{"_id":"MaKw"}],"article_type":"original","scopus_import":"1","_id":"14499","article_processing_charge":"Yes","oa_version":"Published Version","day":"24","external_id":{"arxiv":["2208.02874"],"isi":["001123866200001"]},"date_created":"2023-11-07T09:02:48Z","title":"Anticoncentration in Ramsey graphs and a proof of the Erdős–McKay conjecture","author":[{"orcid":"0000-0002-4003-7567","first_name":"Matthew Alan","last_name":"Kwan","full_name":"Kwan, Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3"},{"full_name":"Sah, Ashwin","first_name":"Ashwin","last_name":"Sah"},{"first_name":"Lisa","last_name":"Sauermann","full_name":"Sauermann, Lisa"},{"last_name":"Sawhney","first_name":"Mehtaab","full_name":"Sawhney, Mehtaab"}],"project":[{"grant_number":"101076777","name":"Randomness and structure in combinatorics","_id":"bd95085b-d553-11ed-ba76-e55d3349be45"}],"abstract":[{"text":"An n-vertex graph is called C-Ramsey if it has no clique or independent set of size Clog2n (i.e., if it has near-optimal Ramsey behavior). In this paper, we study edge statistics in Ramsey graphs, in particular obtaining very precise control of the distribution of the number of edges in a random vertex subset of a C-Ramsey graph. This brings together two ongoing lines of research: the study of ‘random-like’ properties of Ramsey graphs and the study of small-ball probability for low-degree polynomials of independent random variables.\r\n\r\nThe proof proceeds via an ‘additive structure’ dichotomy on the degree sequence and involves a wide range of different tools from Fourier analysis, random matrix theory, the theory of Boolean functions, probabilistic combinatorics and low-rank approximation. In particular, a key ingredient is a new sharpened version of the quadratic Carbery–Wright theorem on small-ball probability for polynomials of Gaussians, which we believe is of independent interest. One of the consequences of our result is the resolution of an old conjecture of Erdős and McKay, for which Erdős reiterated in several of his open problem collections and for which he offered one of his notorious monetary prizes.","lang":"eng"}],"date_updated":"2025-09-09T13:16:15Z","file_date_updated":"2023-11-07T09:16:23Z","publication":"Forum of Mathematics, Pi","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_status":"published","article_number":"e21","corr_author":"1","date_published":"2023-08-24T00:00:00Z","keyword":["Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Analysis"],"volume":11,"status":"public","publication_identifier":{"issn":["2050-5086"]},"acknowledgement":"Kwan was supported for part of this work by ERC Starting Grant ‘RANDSTRUCT’ No. 101076777. Sah and Sawhney were supported by NSF Graduate Research Fellowship Program DGE-2141064. Sah was supported by the PD Soros Fellowship. Sauermann was supported by NSF Award DMS-2100157, and for part of this work by a Sloan Research Fellowship.","type":"journal_article","month":"08","isi":1,"arxiv":1,"language":[{"iso":"eng"}],"file":[{"file_id":"14500","success":1,"creator":"dernst","access_level":"open_access","relation":"main_file","date_created":"2023-11-07T09:16:23Z","checksum":"54b824098d59073cc87a308d458b0a3e","content_type":"application/pdf","file_size":1218719,"date_updated":"2023-11-07T09:16:23Z","file_name":"2023_ForumMathematics_Kwan.pdf"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2023","oa":1,"doi":"10.1017/fmp.2023.17","has_accepted_license":"1"},{"day":"01","_id":"14772","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","scopus_import":"1","article_type":"original","intvolume":"       285","department":[{"_id":"JuFi"}],"publisher":"Elsevier","quality_controlled":"1","citation":{"short":"A. Agresti, A. Hussein, Journal of Functional Analysis 285 (2023).","mla":"Agresti, Antonio, and Amru Hussein. “Maximal Lp-Regularity and H∞-Calculus for Block Operator Matrices and Applications.” <i>Journal of Functional Analysis</i>, vol. 285, no. 11, 110146, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.110146\">10.1016/j.jfa.2023.110146</a>.","ieee":"A. Agresti and A. Hussein, “Maximal Lp-regularity and H∞-calculus for block operator matrices and applications,” <i>Journal of Functional Analysis</i>, vol. 285, no. 11. Elsevier, 2023.","ista":"Agresti A, Hussein A. 2023. Maximal Lp-regularity and H∞-calculus for block operator matrices and applications. Journal of Functional Analysis. 285(11), 110146.","chicago":"Agresti, Antonio, and Amru Hussein. “Maximal Lp-Regularity and H∞-Calculus for Block Operator Matrices and Applications.” <i>Journal of Functional Analysis</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.jfa.2023.110146\">https://doi.org/10.1016/j.jfa.2023.110146</a>.","apa":"Agresti, A., &#38; Hussein, A. (2023). Maximal Lp-regularity and H∞-calculus for block operator matrices and applications. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2023.110146\">https://doi.org/10.1016/j.jfa.2023.110146</a>","ama":"Agresti A, Hussein A. Maximal Lp-regularity and H∞-calculus for block operator matrices and applications. <i>Journal of Functional Analysis</i>. 2023;285(11). doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.110146\">10.1016/j.jfa.2023.110146</a>"},"ddc":["510"],"date_published":"2023-12-01T00:00:00Z","article_number":"110146","corr_author":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","file_date_updated":"2024-01-10T11:23:57Z","publication":"Journal of Functional Analysis","date_updated":"2024-10-09T21:07:48Z","abstract":[{"lang":"eng","text":"Many coupled evolution equations can be described via 2×2-block operator matrices of the form A=[ \r\nA\tB\r\nC\tD\r\n ] in a product space X=X1×X2 with possibly unbounded entries. Here, the case of diagonally dominant block operator matrices is considered, that is, the case where the full operator A can be seen as a relatively bounded perturbation of its diagonal part with D(A)=D(A)×D(D) though with possibly large relative bound. For such operators the properties of sectoriality, R-sectoriality and the boundedness of the H∞-calculus are studied, and for these properties perturbation results for possibly large but structured perturbations are derived. Thereby, the time dependent parabolic problem associated with A can be analyzed in maximal Lpt\r\n-regularity spaces, and this is applied to a wide range of problems such as different theories for liquid crystals, an artificial Stokes system, strongly damped wave and plate equations, and a Keller-Segel model."}],"external_id":{"arxiv":["2108.01962"],"isi":["001081809000001"]},"date_created":"2024-01-10T09:15:18Z","title":"Maximal Lp-regularity and H∞-calculus for block operator matrices and applications","author":[{"orcid":"0000-0002-9573-2962","first_name":"Antonio","last_name":"Agresti","full_name":"Agresti, Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72"},{"full_name":"Hussein, Amru","first_name":"Amru","last_name":"Hussein"}],"type":"journal_article","acknowledgement":"We would like to thank Tim Binz, Emiel Lorist and Mark Veraar for valuable discussions. We also thank the anonymous referees for their helpful comments and suggestions, and for the very accurate reading of the manuscript.\r\nThe first author has been supported partially by the Nachwuchsring – Network for the promotion of young scientists – at TU Kaiserslautern. Both authors have been supported by MathApp – Mathematics Applied to Real-World Problems - part of the Research Initiative of the Federal State of Rhineland-Palatinate, Germany.","publication_identifier":{"issn":["0022-1236"]},"status":"public","volume":285,"keyword":["Analysis"],"doi":"10.1016/j.jfa.2023.110146","issue":"11","has_accepted_license":"1","year":"2023","oa":1,"file":[{"date_created":"2024-01-10T11:23:57Z","relation":"main_file","checksum":"eda98ca2aa73da91bd074baed34c2b3c","file_size":1120592,"content_type":"application/pdf","date_updated":"2024-01-10T11:23:57Z","file_name":"2023_JourFunctionalAnalysis_Agresti.pdf","file_id":"14789","access_level":"open_access","success":1,"creator":"dernst"}],"language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"isi":1,"arxiv":1,"month":"12"},{"date_published":"2022-10-15T00:00:00Z","article_number":"111439","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","publication":"Journal of Computational Physics","date_updated":"2024-10-21T06:01:47Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2103.09481"}],"abstract":[{"text":"We revisit two basic Direct Simulation Monte Carlo Methods to model aggregation kinetics and extend them for aggregation processes with collisional fragmentation (shattering). We test the performance and accuracy of the extended methods and compare their performance with efficient deterministic finite-difference method applied to the same model. We validate the stochastic methods on the test problems and apply them to verify the existence of oscillating regimes in the aggregation-fragmentation kinetics recently detected in deterministic simulations. We confirm the emergence of steady oscillations of densities in such systems and prove the stability of the\r\noscillations with respect to fluctuations and noise.","lang":"eng"}],"date_created":"2022-07-11T12:19:59Z","external_id":{"arxiv":["2103.09481"],"isi":["000917225500013"]},"title":"Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics","author":[{"full_name":"Kalinov, Aleksei","id":"44b7120e-eb97-11eb-a6c2-e1557aa81d02","last_name":"Kalinov","first_name":"Aleksei","orcid":"0000-0003-2189-3904"},{"first_name":"A.I.","last_name":"Osinskiy","full_name":"Osinskiy, A.I."},{"first_name":"S.A.","last_name":"Matveev","full_name":"Matveev, S.A."},{"full_name":"Otieno, W.","last_name":"Otieno","first_name":"W."},{"full_name":"Brilliantov, N.V.","last_name":"Brilliantov","first_name":"N.V."}],"day":"15","_id":"11556","article_processing_charge":"No","oa_version":"Preprint","scopus_import":"1","article_type":"original","intvolume":"       467","department":[{"_id":"GradSch"},{"_id":"ChWo"}],"publisher":"Elsevier","quality_controlled":"1","citation":{"ama":"Kalinov A, Osinskiy AI, Matveev SA, Otieno W, Brilliantov NV. Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics. <i>Journal of Computational Physics</i>. 2022;467. doi:<a href=\"https://doi.org/10.1016/j.jcp.2022.111439\">10.1016/j.jcp.2022.111439</a>","apa":"Kalinov, A., Osinskiy, A. I., Matveev, S. A., Otieno, W., &#38; Brilliantov, N. V. (2022). Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics. <i>Journal of Computational Physics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jcp.2022.111439\">https://doi.org/10.1016/j.jcp.2022.111439</a>","chicago":"Kalinov, Aleksei, A.I. Osinskiy, S.A. Matveev, W. Otieno, and N.V. Brilliantov. “Direct Simulation Monte Carlo for New Regimes in Aggregation-Fragmentation Kinetics.” <i>Journal of Computational Physics</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.jcp.2022.111439\">https://doi.org/10.1016/j.jcp.2022.111439</a>.","ista":"Kalinov A, Osinskiy AI, Matveev SA, Otieno W, Brilliantov NV. 2022. Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics. Journal of Computational Physics. 467, 111439.","short":"A. Kalinov, A.I. Osinskiy, S.A. Matveev, W. Otieno, N.V. Brilliantov, Journal of Computational Physics 467 (2022).","mla":"Kalinov, Aleksei, et al. “Direct Simulation Monte Carlo for New Regimes in Aggregation-Fragmentation Kinetics.” <i>Journal of Computational Physics</i>, vol. 467, 111439, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.jcp.2022.111439\">10.1016/j.jcp.2022.111439</a>.","ieee":"A. Kalinov, A. I. Osinskiy, S. A. Matveev, W. Otieno, and N. V. Brilliantov, “Direct simulation Monte Carlo for new regimes in aggregation-fragmentation kinetics,” <i>Journal of Computational Physics</i>, vol. 467. Elsevier, 2022."},"ddc":["518"],"doi":"10.1016/j.jcp.2022.111439","year":"2022","oa":1,"language":[{"iso":"eng"}],"isi":1,"arxiv":1,"month":"10","type":"journal_article","acknowledgement":"Zhores supercomputer of Skolkovo Institute of Science and Technology [68] has been used in the present research. S.A.M. was supported by Moscow Center for Fundamental and Applied Mathematics (the agreement with the Ministry of Education and Science of the Russian Federation No. 075-15-2019-1624). A.I.O. acknowledges RFBR project No. 20-31-90022. N.V.B. acknowledges the support of the Analytical Center (subsidy agreement 000000D730321P5Q0002, Grant No. 70-2021-00145 02.11.2021).","publication_identifier":{"issn":["0021-9991"]},"status":"public","volume":467,"keyword":["Computer Science Applications","Physics and Astronomy (miscellaneous)","Applied Mathematics","Computational Mathematics","Modeling and Simulation","Numerical Analysis"]},{"month":"07","issue":"3","doi":"10.1007/s43036-022-00199-w","has_accepted_license":"1","file":[{"relation":"main_file","date_created":"2022-08-18T08:02:34Z","file_name":"2022_AdvancesOperatorTheory_Wirth.pdf","date_updated":"2022-08-18T08:02:34Z","file_size":389060,"content_type":"application/pdf","checksum":"913474844a1b38264fb710746d5e2e98","file_id":"11921","creator":"dernst","success":1,"access_level":"open_access"}],"language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2022","oa":1,"status":"public","publication_identifier":{"eissn":["2538-225X"]},"keyword":["Algebra and Number Theory","Analysis"],"volume":7,"type":"journal_article","acknowledgement":"The author was supported by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes) and by the German Research Foundation (DFG) via RTG 1523/2. The author would like to thank Daniel Lenz for his support and encouragement during the author’s ongoing graduate studies and him as well as Marcel Schmidt for fruitful discussions on domination of quadratic forms. He wants to thank Batu Güneysu and Peter Stollmann for valuable comments on a preliminary version of this article. He would also like to thank the organizers of the conference Analysis and Geometry on Graphs and Manifolds in Potsdam, where the initial motivation of this article was conceived, and the organizers of the intense activity period Metric Measure Spaces and Ricci Curvature at MPIM in Bonn, where this work was finished.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","abstract":[{"text":"A domain is called Kac regular for a quadratic form on L2 if every functions vanishing almost everywhere outside the domain can be approximated in form norm by functions with compact support in the domain. It is shown that this notion is stable under domination of quadratic forms. As applications measure perturbations of quasi-regular Dirichlet forms, Cheeger energies on metric measure spaces and Schrödinger operators on manifolds are studied. Along the way a characterization of the Sobolev space with Dirichlet boundary conditions on domains in infinitesimally Riemannian metric measure spaces is obtained.","lang":"eng"}],"date_updated":"2024-10-09T21:03:07Z","date_created":"2022-08-18T07:22:24Z","title":"Kac regularity and domination of quadratic forms","author":[{"id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","full_name":"Wirth, Melchior","orcid":"0000-0002-0519-4241","last_name":"Wirth","first_name":"Melchior"}],"article_number":"38","corr_author":"1","date_published":"2022-07-01T00:00:00Z","file_date_updated":"2022-08-18T08:02:34Z","publication":"Advances in Operator Theory","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","publisher":"Springer Nature","ddc":["510"],"citation":{"apa":"Wirth, M. (2022). Kac regularity and domination of quadratic forms. <i>Advances in Operator Theory</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s43036-022-00199-w\">https://doi.org/10.1007/s43036-022-00199-w</a>","ama":"Wirth M. Kac regularity and domination of quadratic forms. <i>Advances in Operator Theory</i>. 2022;7(3). doi:<a href=\"https://doi.org/10.1007/s43036-022-00199-w\">10.1007/s43036-022-00199-w</a>","chicago":"Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” <i>Advances in Operator Theory</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s43036-022-00199-w\">https://doi.org/10.1007/s43036-022-00199-w</a>.","ista":"Wirth M. 2022. Kac regularity and domination of quadratic forms. Advances in Operator Theory. 7(3), 38.","short":"M. Wirth, Advances in Operator Theory 7 (2022).","mla":"Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” <i>Advances in Operator Theory</i>, vol. 7, no. 3, 38, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s43036-022-00199-w\">10.1007/s43036-022-00199-w</a>.","ieee":"M. Wirth, “Kac regularity and domination of quadratic forms,” <i>Advances in Operator Theory</i>, vol. 7, no. 3. Springer Nature, 2022."},"quality_controlled":"1","_id":"11916","oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","day":"01","intvolume":"         7","department":[{"_id":"JaMa"}],"scopus_import":"1","article_type":"original"},{"article_type":"original","scopus_import":"1","intvolume":"        10","department":[{"_id":"LaEr"}],"day":"27","_id":"12148","oa_version":"Published Version","article_processing_charge":"No","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022).","mla":"Cipolloni, Giorgio, et al. “Rank-Uniform Local Law for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>, vol. 10, e96, Cambridge University Press, 2022, doi:<a href=\"https://doi.org/10.1017/fms.2022.86\">10.1017/fms.2022.86</a>.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner matrices,” <i>Forum of Mathematics, Sigma</i>, vol. 10. Cambridge University Press, 2022.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 10, e96.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Rank-Uniform Local Law for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2022. <a href=\"https://doi.org/10.1017/fms.2022.86\">https://doi.org/10.1017/fms.2022.86</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Rank-uniform local law for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2022;10. doi:<a href=\"https://doi.org/10.1017/fms.2022.86\">10.1017/fms.2022.86</a>","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Rank-uniform local law for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2022.86\">https://doi.org/10.1017/fms.2022.86</a>"},"quality_controlled":"1","ddc":["510"],"publisher":"Cambridge University Press","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","file_date_updated":"2023-01-24T10:02:40Z","publication":"Forum of Mathematics, Sigma","date_published":"2022-10-27T00:00:00Z","article_number":"e96","corr_author":"1","project":[{"call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"external_id":{"isi":["000873719200001"]},"date_created":"2023-01-12T12:07:30Z","author":[{"last_name":"Cipolloni","first_name":"Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László"},{"full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","first_name":"Dominik J","last_name":"Schröder"}],"title":"Rank-uniform local law for Wigner matrices","date_updated":"2025-04-14T07:57:18Z","abstract":[{"text":"We prove a general local law for Wigner matrices that optimally handles observables of arbitrary rank and thus unifies the well-known averaged and isotropic local laws. As an application, we prove a central limit theorem in quantum unique ergodicity (QUE): that is, we show that the quadratic forms of a general deterministic matrix A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation. For the bulk spectrum, we thus generalise our previous result [17] as valid for test matrices A of large rank as well as the result of Benigni and Lopatto [7] as valid for specific small-rank observables.","lang":"eng"}],"acknowledgement":"L.E. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331. D.S. acknowledges the support of Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","type":"journal_article","volume":10,"keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"publication_identifier":{"issn":["2050-5094"]},"status":"public","ec_funded":1,"year":"2022","oa":1,"file":[{"success":1,"creator":"dernst","access_level":"open_access","file_id":"12356","checksum":"94a049aeb1eea5497aa097712a73c400","file_size":817089,"content_type":"application/pdf","date_updated":"2023-01-24T10:02:40Z","file_name":"2022_ForumMath_Cipolloni.pdf","relation":"main_file","date_created":"2023-01-24T10:02:40Z"}],"language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"doi":"10.1017/fms.2022.86","has_accepted_license":"1","month":"10","isi":1},{"type":"journal_article","volume":43,"keyword":["Analysis"],"publication_identifier":{"issn":["0895-4798"],"eissn":["1095-7162"]},"status":"public","year":"2022","oa":1,"language":[{"iso":"eng"}],"doi":"10.1137/21m1424408","issue":"3","page":"1469-1487","month":"07","isi":1,"arxiv":1,"scopus_import":"1","article_type":"original","intvolume":"        43","department":[{"_id":"LaEr"}],"day":"01","_id":"12179","oa_version":"Preprint","article_processing_charge":"No","citation":{"apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). On the condition number of the shifted real Ginibre ensemble. <i>SIAM Journal on Matrix Analysis and Applications</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/21m1424408\">https://doi.org/10.1137/21m1424408</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. On the condition number of the shifted real Ginibre ensemble. <i>SIAM Journal on Matrix Analysis and Applications</i>. 2022;43(3):1469-1487. doi:<a href=\"https://doi.org/10.1137/21m1424408\">10.1137/21m1424408</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Condition Number of the Shifted Real Ginibre Ensemble.” <i>SIAM Journal on Matrix Analysis and Applications</i>. Society for Industrial and Applied Mathematics, 2022. <a href=\"https://doi.org/10.1137/21m1424408\">https://doi.org/10.1137/21m1424408</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. On the condition number of the shifted real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. 43(3), 1469–1487.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “On the condition number of the shifted real Ginibre ensemble,” <i>SIAM Journal on Matrix Analysis and Applications</i>, vol. 43, no. 3. Society for Industrial and Applied Mathematics, pp. 1469–1487, 2022.","mla":"Cipolloni, Giorgio, et al. “On the Condition Number of the Shifted Real Ginibre Ensemble.” <i>SIAM Journal on Matrix Analysis and Applications</i>, vol. 43, no. 3, Society for Industrial and Applied Mathematics, 2022, pp. 1469–87, doi:<a href=\"https://doi.org/10.1137/21m1424408\">10.1137/21m1424408</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, SIAM Journal on Matrix Analysis and Applications 43 (2022) 1469–1487."},"quality_controlled":"1","publisher":"Society for Industrial and Applied Mathematics","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_status":"published","publication":"SIAM Journal on Matrix Analysis and Applications","date_published":"2022-07-01T00:00:00Z","corr_author":"1","date_created":"2023-01-12T12:12:38Z","external_id":{"isi":["001125796400002"],"arxiv":["2105.13719"]},"title":"On the condition number of the shifted real Ginibre ensemble","author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","first_name":"Giorgio","last_name":"Cipolloni"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J"}],"date_updated":"2025-09-10T09:51:27Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2105.13719","open_access":"1"}],"abstract":[{"lang":"eng","text":"We derive an accurate lower tail estimate on the lowest singular value σ1(X−z) of a real Gaussian (Ginibre) random matrix X shifted by a complex parameter z. Such shift effectively changes the upper tail behavior of the condition number κ(X−z) from the slower (κ(X−z)≥t)≲1/t decay typical for real Ginibre matrices to the faster 1/t2 decay seen for complex Ginibre matrices as long as z is away from the real axis. This sharpens and resolves a recent conjecture in [J. Banks et al., https://arxiv.org/abs/2005.08930, 2020] on the regularizing effect of the real Ginibre ensemble with a genuinely complex shift. As a consequence we obtain an improved upper bound on the eigenvalue condition numbers (known also as the eigenvector overlaps) for real Ginibre matrices. The main technical tool is a rigorous supersymmetric analysis from our earlier work [Probab. Math. Phys., 1 (2020), pp. 101--146]."}]},{"language":[{"iso":"eng"}],"file":[{"file_id":"12415","creator":"dernst","success":1,"access_level":"open_access","relation":"main_file","date_created":"2023-01-27T08:08:39Z","date_updated":"2023-01-27T08:08:39Z","file_name":"2022_LinearAlgebra_Carlen.pdf","checksum":"cf3cb7e7e34baa967849f01d8f0c1ae4","file_size":441184,"content_type":"application/pdf"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2022","oa":1,"doi":"10.1016/j.laa.2022.09.001","has_accepted_license":"1","page":"289-310","month":"12","isi":1,"acknowledgement":"Work partially supported by the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337.","type":"journal_article","keyword":["Discrete Mathematics and Combinatorics","Geometry and Topology","Numerical Analysis","Algebra and Number Theory"],"volume":654,"status":"public","publication_identifier":{"issn":["0024-3795"]},"file_date_updated":"2023-01-27T08:08:39Z","publication":"Linear Algebra and its Applications","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","corr_author":"1","date_published":"2022-12-01T00:00:00Z","date_created":"2023-01-16T09:46:38Z","external_id":{"isi":["000860689600014"]},"title":"Monotonicity versions of Epstein's concavity theorem and related inequalities","author":[{"first_name":"Eric A.","last_name":"Carlen","full_name":"Carlen, Eric A."},{"last_name":"Zhang","first_name":"Haonan","full_name":"Zhang, Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425"}],"project":[{"grant_number":"M03337","name":"Curvature-dimension in noncommutative analysis","_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6"}],"abstract":[{"text":"Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The latter says that quantum operations can never increase the relative entropy. The monotonicity versions often have many advantages, and often have direct physical application, as in the example just mentioned. Moreover, the monotonicity results are often valid for a larger class of maps than, say, quantum operations (which are completely positive). In this paper we prove several new monotonicity results, the first of which is a monotonicity theorem that has as a simple corollary a celebrated concavity theorem of Epstein. Our starting points are the monotonicity versions of the Lieb Concavity and the Lieb Convexity Theorems. We also give two new proofs of these in their general forms using interpolation. We then prove our new monotonicity theorems by several duality arguments.","lang":"eng"}],"date_updated":"2025-04-14T13:05:27Z","intvolume":"       654","department":[{"_id":"JaMa"}],"article_type":"original","scopus_import":"1","_id":"12216","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","day":"01","ddc":["510"],"citation":{"apa":"Carlen, E. A., &#38; Zhang, H. (2022). Monotonicity versions of Epstein’s concavity theorem and related inequalities. <i>Linear Algebra and Its Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.laa.2022.09.001\">https://doi.org/10.1016/j.laa.2022.09.001</a>","ama":"Carlen EA, Zhang H. Monotonicity versions of Epstein’s concavity theorem and related inequalities. <i>Linear Algebra and its Applications</i>. 2022;654:289-310. doi:<a href=\"https://doi.org/10.1016/j.laa.2022.09.001\">10.1016/j.laa.2022.09.001</a>","chicago":"Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s Concavity Theorem and Related Inequalities.” <i>Linear Algebra and Its Applications</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.laa.2022.09.001\">https://doi.org/10.1016/j.laa.2022.09.001</a>.","ista":"Carlen EA, Zhang H. 2022. Monotonicity versions of Epstein’s concavity theorem and related inequalities. Linear Algebra and its Applications. 654, 289–310.","ieee":"E. A. Carlen and H. Zhang, “Monotonicity versions of Epstein’s concavity theorem and related inequalities,” <i>Linear Algebra and its Applications</i>, vol. 654. Elsevier, pp. 289–310, 2022.","short":"E.A. Carlen, H. Zhang, Linear Algebra and Its Applications 654 (2022) 289–310.","mla":"Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s Concavity Theorem and Related Inequalities.” <i>Linear Algebra and Its Applications</i>, vol. 654, Elsevier, 2022, pp. 289–310, doi:<a href=\"https://doi.org/10.1016/j.laa.2022.09.001\">10.1016/j.laa.2022.09.001</a>."},"quality_controlled":"1","publisher":"Elsevier"},{"page":"1394-1434","issue":"7","doi":"10.1080/03605302.2022.2056702","language":[{"iso":"eng"}],"oa":1,"year":"2022","arxiv":1,"isi":1,"month":"07","type":"journal_article","acknowledgement":"N. De Nitti acknowledges the kind hospitality of IST Austria within the framework of the ISTernship Summer Program 2018, during which most of the present article was written. N. DeNitti has received funding by The Austrian Agency for International Cooperation in Education &Research (OeAD-GmbH) via its financial support of the ISTernship Summer Program 2018. N.De Nitti would also like to thank Giuseppe Coclite, Giuseppe Devillanova, Giuseppe Florio, Sebastian Hensel, and Francesco Maddalena for several helpful conversations on topics related to this work.","status":"public","publication_identifier":{"eissn":["1532-4133"],"issn":["0360-5302"]},"keyword":["Applied Mathematics","Analysis"],"volume":47,"corr_author":"1","date_published":"2022-07-01T00:00:00Z","publication":"Communications in Partial Differential Equations","publication_status":"published","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","abstract":[{"text":"We establish sharp criteria for the instantaneous propagation of free boundaries in solutions to the thin-film equation. The criteria are formulated in terms of the initial distribution of mass (as opposed to previous almost-optimal results), reflecting the fact that mass is a locally conserved quantity for the thin-film equation. In the regime of weak slippage, our criteria are at the same time necessary and sufficient. The proof of our upper bounds on free boundary propagation is based on a strategy of “propagation of degeneracy” down to arbitrarily small spatial scales: We combine estimates on the local mass and estimates on energies to show that “degeneracy” on a certain space-time cylinder entails “degeneracy” on a spatially smaller space-time cylinder with the same time horizon. The derivation of our lower bounds on free boundary propagation is based on a combination of a monotone quantity and almost optimal estimates established previously by the second author with a new estimate connecting motion of mass to entropy production.","lang":"eng"}],"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.1907.05342","open_access":"1"}],"date_updated":"2024-10-09T21:03:57Z","title":"Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation","author":[{"last_name":"De Nitti","first_name":"Nicola","full_name":"De Nitti, Nicola"},{"full_name":"Fischer, Julian L","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","last_name":"Fischer","first_name":"Julian L","orcid":"0000-0002-0479-558X"}],"date_created":"2023-01-16T10:06:50Z","external_id":{"arxiv":["1907.05342"],"isi":["000805689800001"]},"article_processing_charge":"No","oa_version":"Preprint","_id":"12304","day":"01","department":[{"_id":"JuFi"}],"intvolume":"        47","scopus_import":"1","article_type":"original","publisher":"Taylor & Francis","citation":{"ama":"De Nitti N, Fischer JL. Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation. <i>Communications in Partial Differential Equations</i>. 2022;47(7):1394-1434. doi:<a href=\"https://doi.org/10.1080/03605302.2022.2056702\">10.1080/03605302.2022.2056702</a>","apa":"De Nitti, N., &#38; Fischer, J. L. (2022). Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation. <i>Communications in Partial Differential Equations</i>. Taylor &#38; Francis. <a href=\"https://doi.org/10.1080/03605302.2022.2056702\">https://doi.org/10.1080/03605302.2022.2056702</a>","chicago":"De Nitti, Nicola, and Julian L Fischer. “Sharp Criteria for the Waiting Time Phenomenon in Solutions to the Thin-Film Equation.” <i>Communications in Partial Differential Equations</i>. Taylor &#38; Francis, 2022. <a href=\"https://doi.org/10.1080/03605302.2022.2056702\">https://doi.org/10.1080/03605302.2022.2056702</a>.","ista":"De Nitti N, Fischer JL. 2022. Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation. Communications in Partial Differential Equations. 47(7), 1394–1434.","mla":"De Nitti, Nicola, and Julian L. Fischer. “Sharp Criteria for the Waiting Time Phenomenon in Solutions to the Thin-Film Equation.” <i>Communications in Partial Differential Equations</i>, vol. 47, no. 7, Taylor &#38; Francis, 2022, pp. 1394–434, doi:<a href=\"https://doi.org/10.1080/03605302.2022.2056702\">10.1080/03605302.2022.2056702</a>.","short":"N. De Nitti, J.L. Fischer, Communications in Partial Differential Equations 47 (2022) 1394–1434.","ieee":"N. De Nitti and J. L. Fischer, “Sharp criteria for the waiting time phenomenon in solutions to the thin-film equation,” <i>Communications in Partial Differential Equations</i>, vol. 47, no. 7. Taylor &#38; Francis, pp. 1394–1434, 2022."},"quality_controlled":"1"},{"arxiv":1,"isi":1,"month":"01","page":"114-172","issue":"1","doi":"10.1137/21m1424925","language":[{"iso":"eng"}],"oa":1,"year":"2022","status":"public","publication_identifier":{"issn":["0036-1410"],"eissn":["1095-7154"]},"keyword":["Applied Mathematics","Computational Mathematics","Analysis"],"volume":54,"type":"journal_article","abstract":[{"lang":"eng","text":"This paper is concerned with the sharp interface limit for the Allen--Cahn equation with a nonlinear Robin boundary condition in a bounded smooth domain Ω⊂\\R2. We assume that a diffuse interface already has developed and that it is in contact with the boundary ∂Ω. The boundary condition is designed in such a way that the limit problem is given by the mean curvature flow with constant α-contact angle. For α close to 90° we prove a local in time convergence result for well-prepared initial data for times when a smooth solution to the limit problem exists. Based on the latter we construct a suitable curvilinear coordinate system and carry out a rigorous asymptotic expansion for the Allen--Cahn equation with the nonlinear Robin boundary condition. Moreover, we show a spectral estimate for the corresponding linearized Allen--Cahn operator and with its aid we derive strong norm estimates for the difference of the exact and approximate solutions using a Gronwall-type argument."}],"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2105.08434","open_access":"1"}],"date_updated":"2024-10-09T21:03:58Z","title":"Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°","author":[{"last_name":"Abels","first_name":"Helmut","full_name":"Abels, Helmut"},{"full_name":"Moser, Maximilian","id":"a60047a9-da77-11eb-85b4-c4dc385ebb8c","last_name":"Moser","first_name":"Maximilian"}],"date_created":"2023-01-16T10:07:00Z","external_id":{"isi":["000762768000004"],"arxiv":["2105.08434"]},"corr_author":"1","date_published":"2022-01-04T00:00:00Z","publication":"SIAM Journal on Mathematical Analysis","publication_status":"published","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Society for Industrial and Applied Mathematics","quality_controlled":"1","citation":{"chicago":"Abels, Helmut, and Maximilian Moser. “Convergence of the Allen--Cahn Equation with a Nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact Angle Close to 90°.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics, 2022. <a href=\"https://doi.org/10.1137/21m1424925\">https://doi.org/10.1137/21m1424925</a>.","ama":"Abels H, Moser M. Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°. <i>SIAM Journal on Mathematical Analysis</i>. 2022;54(1):114-172. doi:<a href=\"https://doi.org/10.1137/21m1424925\">10.1137/21m1424925</a>","apa":"Abels, H., &#38; Moser, M. (2022). Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/21m1424925\">https://doi.org/10.1137/21m1424925</a>","ieee":"H. Abels and M. Moser, “Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 1. Society for Industrial and Applied Mathematics, pp. 114–172, 2022.","mla":"Abels, Helmut, and Maximilian Moser. “Convergence of the Allen--Cahn Equation with a Nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact Angle Close to 90°.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 1, Society for Industrial and Applied Mathematics, 2022, pp. 114–72, doi:<a href=\"https://doi.org/10.1137/21m1424925\">10.1137/21m1424925</a>.","short":"H. Abels, M. Moser, SIAM Journal on Mathematical Analysis 54 (2022) 114–172.","ista":"Abels H, Moser M. 2022. Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition to mean curvature flow with contact angle close to 90°. SIAM Journal on Mathematical Analysis. 54(1), 114–172."},"oa_version":"Preprint","article_processing_charge":"No","_id":"12305","day":"04","department":[{"_id":"JuFi"}],"intvolume":"        54","scopus_import":"1","article_type":"original"},{"volume":10,"keyword":["computational mathematics","discrete mathematics and combinatorics","geometry and topology","mathematical physics","statistics and probability","algebra and number theory","theoretical computer science","analysis"],"publication_identifier":{"eissn":["2050-5094"]},"ec_funded":1,"status":"public","acknowledgement":"J.H. acknowledges partial financial support by the ERC Advanced Grant ‘RMTBeyond’ No. 101020331. Support for publication costs from the Deutsche Forschungsgemeinschaft and the Open Access Publishing Fund of the University of Tübingen is gratefully acknowledged.","type":"journal_article","month":"01","arxiv":1,"isi":1,"oa":1,"year":"2022","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"file":[{"date_created":"2022-01-19T09:27:43Z","relation":"main_file","date_updated":"2022-01-19T09:27:43Z","file_name":"2022_ForumMathSigma_Henheik.pdf","file_size":705323,"content_type":"application/pdf","checksum":"87592a755adcef22ea590a99dc728dd3","file_id":"10646","access_level":"open_access","creator":"cchlebak","success":1}],"language":[{"iso":"eng"}],"has_accepted_license":"1","doi":"10.1017/fms.2021.80","quality_controlled":"1","citation":{"ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. <i>Forum of Mathematics, Sigma</i>. 2022;10. doi:<a href=\"https://doi.org/10.1017/fms.2021.80\">10.1017/fms.2021.80</a>","apa":"Henheik, S. J., &#38; Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2021.80\">https://doi.org/10.1017/fms.2021.80</a>","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2022. <a href=\"https://doi.org/10.1017/fms.2021.80\">https://doi.org/10.1017/fms.2021.80</a>.","ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 10, e4.","ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk,” <i>Forum of Mathematics, Sigma</i>, vol. 10. Cambridge University Press, 2022.","short":"S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022).","mla":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” <i>Forum of Mathematics, Sigma</i>, vol. 10, e4, Cambridge University Press, 2022, doi:<a href=\"https://doi.org/10.1017/fms.2021.80\">10.1017/fms.2021.80</a>."},"ddc":["510"],"publisher":"Cambridge University Press","scopus_import":"1","article_type":"original","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"intvolume":"        10","day":"18","oa_version":"Published Version","article_processing_charge":"Yes","_id":"10643","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"title":"Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","last_name":"Henheik"},{"last_name":"Teufel","first_name":"Stefan","full_name":"Teufel, Stefan"}],"date_created":"2022-01-18T16:18:51Z","external_id":{"isi":["000743615000001"],"arxiv":["2012.15239"]},"date_updated":"2025-04-14T07:57:17Z","abstract":[{"lang":"eng","text":"We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap.\r\n\r\n"}],"publication_status":"published","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file_date_updated":"2022-01-19T09:27:43Z","publication":"Forum of Mathematics, Sigma","date_published":"2022-01-18T00:00:00Z","corr_author":"1","article_number":"e4"},{"publication":"Foundations of Computational Mathematics","file_date_updated":"2021-12-13T15:47:54Z","publication_status":"published","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_published":"2022-10-01T00:00:00Z","title":"Optimal combination of linear and spectral estimators for generalized linear models","author":[{"orcid":"0000-0002-3242-7020","last_name":"Mondelli","first_name":"Marco","full_name":"Mondelli, Marco","id":"27EB676C-8706-11E9-9510-7717E6697425"},{"full_name":"Thrampoulidis, Christos","last_name":"Thrampoulidis","first_name":"Christos"},{"last_name":"Venkataramanan","first_name":"Ramji","full_name":"Venkataramanan, Ramji"}],"date_created":"2021-11-03T10:59:08Z","external_id":{"isi":["000685721000001"],"arxiv":["2008.03326"]},"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"abstract":[{"lang":"eng","text":"We study the problem of recovering an unknown signal 𝑥𝑥 given measurements obtained from a generalized linear model with a Gaussian sensing matrix. Two popular solutions are based on a linear estimator 𝑥𝑥^L and a spectral estimator 𝑥𝑥^s. The former is a data-dependent linear combination of the columns of the measurement matrix, and its analysis is quite simple. The latter is the principal eigenvector of a data-dependent matrix, and a recent line of work has studied its performance. In this paper, we show how to optimally combine 𝑥𝑥^L and 𝑥𝑥^s. At the heart of our analysis is the exact characterization of the empirical joint distribution of (𝑥𝑥,𝑥𝑥^L,𝑥𝑥^s) in the high-dimensional limit. This allows us to compute the Bayes-optimal combination of 𝑥𝑥^L and 𝑥𝑥^s, given the limiting distribution of the signal 𝑥𝑥. When the distribution of the signal is Gaussian, then the Bayes-optimal combination has the form 𝜃𝑥𝑥^L+𝑥𝑥^s and we derive the optimal combination coefficient. In order to establish the limiting distribution of (𝑥𝑥,𝑥𝑥^L,𝑥𝑥^s), we design and analyze an approximate message passing algorithm whose iterates give 𝑥𝑥^L and approach 𝑥𝑥^s. Numerical simulations demonstrate the improvement of the proposed combination with respect to the two methods considered separately."}],"date_updated":"2025-04-15T06:53:08Z","department":[{"_id":"MaMo"}],"intvolume":"        22","scopus_import":"1","article_type":"original","oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","_id":"10211","day":"01","ddc":["510"],"citation":{"chicago":"Mondelli, Marco, Christos Thrampoulidis, and Ramji Venkataramanan. “Optimal Combination of Linear and Spectral Estimators for Generalized Linear Models.” <i>Foundations of Computational Mathematics</i>. Springer, 2022. <a href=\"https://doi.org/10.1007/s10208-021-09531-x\">https://doi.org/10.1007/s10208-021-09531-x</a>.","apa":"Mondelli, M., Thrampoulidis, C., &#38; Venkataramanan, R. (2022). Optimal combination of linear and spectral estimators for generalized linear models. <i>Foundations of Computational Mathematics</i>. Springer. <a href=\"https://doi.org/10.1007/s10208-021-09531-x\">https://doi.org/10.1007/s10208-021-09531-x</a>","ama":"Mondelli M, Thrampoulidis C, Venkataramanan R. Optimal combination of linear and spectral estimators for generalized linear models. <i>Foundations of Computational Mathematics</i>. 2022;22(5):1513-1566. doi:<a href=\"https://doi.org/10.1007/s10208-021-09531-x\">10.1007/s10208-021-09531-x</a>","ieee":"M. Mondelli, C. Thrampoulidis, and R. Venkataramanan, “Optimal combination of linear and spectral estimators for generalized linear models,” <i>Foundations of Computational Mathematics</i>, vol. 22, no. 5. Springer, pp. 1513–1566, 2022.","short":"M. Mondelli, C. Thrampoulidis, R. Venkataramanan, Foundations of Computational Mathematics 22 (2022) 1513–1566.","mla":"Mondelli, Marco, et al. “Optimal Combination of Linear and Spectral Estimators for Generalized Linear Models.” <i>Foundations of Computational Mathematics</i>, vol. 22, no. 5, Springer, 2022, pp. 1513–66, doi:<a href=\"https://doi.org/10.1007/s10208-021-09531-x\">10.1007/s10208-021-09531-x</a>.","ista":"Mondelli M, Thrampoulidis C, Venkataramanan R. 2022. Optimal combination of linear and spectral estimators for generalized linear models. Foundations of Computational Mathematics. 22(5), 1513–1566."},"quality_controlled":"1","publisher":"Springer","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"file":[{"creator":"alisjak","success":1,"access_level":"open_access","file_id":"10542","file_name":"2021_Springer_Mondelli.pdf","date_updated":"2021-12-13T15:47:54Z","checksum":"9ea12dd8045a0678000a3a59295221cb","content_type":"application/pdf","file_size":2305731,"relation":"main_file","date_created":"2021-12-13T15:47:54Z"}],"language":[{"iso":"eng"}],"oa":1,"year":"2022","has_accepted_license":"1","page":"1513-1566","doi":"10.1007/s10208-021-09531-x","issue":"5","month":"10","arxiv":1,"isi":1,"acknowledgement":"M. Mondelli would like to thank Andrea Montanari for helpful discussions. All the authors would like to thank the anonymous reviewers for their helpful comments.","type":"journal_article","keyword":["Applied Mathematics","Computational Theory and Mathematics","Computational Mathematics","Analysis"],"volume":22,"status":"public","publication_identifier":{"issn":["1615-3375"],"eissn":["1615-3383"]}},{"publication":"Journal of Functional Analysis","file_date_updated":"2022-08-02T10:37:55Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","article_number":"109455","corr_author":"1","date_published":"2022-06-15T00:00:00Z","date_created":"2022-03-16T08:41:53Z","external_id":{"isi":["000795160200009"],"arxiv":["2105.04874"]},"author":[{"id":"5DA90512-D80F-11E9-8994-2E2EE6697425","full_name":"Roos, Barbara","orcid":"0000-0002-9071-5880","first_name":"Barbara","last_name":"Roos"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer","first_name":"Robert"}],"title":"Two-particle bound states at interfaces and corners","project":[{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"abstract":[{"text":"We study two interacting quantum particles forming a bound state in d-dimensional free\r\nspace, and constrain the particles in k directions to (0, ∞)k ×Rd−k, with Neumann boundary\r\nconditions. First, we prove that the ground state energy strictly decreases upon going from k\r\nto k+1. This shows that the particles stick to the corner where all boundary planes intersect.\r\nSecond, we show that for all k the resulting Hamiltonian, after removing the free part of the\r\nkinetic energy, has only finitely many eigenvalues below the essential spectrum. This paper\r\ngeneralizes the work of Egger, Kerner and Pankrashkin (J. Spectr. Theory 10(4):1413–1444,\r\n2020) to dimensions d > 1.","lang":"eng"}],"date_updated":"2026-04-07T13:27:39Z","intvolume":"       282","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"scopus_import":"1","article_type":"original","_id":"10850","oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","day":"15","ddc":["510"],"citation":{"ista":"Roos B, Seiringer R. 2022. Two-particle bound states at interfaces and corners. Journal of Functional Analysis. 282(12), 109455.","ieee":"B. Roos and R. Seiringer, “Two-particle bound states at interfaces and corners,” <i>Journal of Functional Analysis</i>, vol. 282, no. 12. Elsevier, 2022.","short":"B. Roos, R. Seiringer, Journal of Functional Analysis 282 (2022).","mla":"Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces and Corners.” <i>Journal of Functional Analysis</i>, vol. 282, no. 12, 109455, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109455\">10.1016/j.jfa.2022.109455</a>.","ama":"Roos B, Seiringer R. Two-particle bound states at interfaces and corners. <i>Journal of Functional Analysis</i>. 2022;282(12). doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109455\">10.1016/j.jfa.2022.109455</a>","apa":"Roos, B., &#38; Seiringer, R. (2022). Two-particle bound states at interfaces and corners. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2022.109455\">https://doi.org/10.1016/j.jfa.2022.109455</a>","chicago":"Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces and Corners.” <i>Journal of Functional Analysis</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.jfa.2022.109455\">https://doi.org/10.1016/j.jfa.2022.109455</a>."},"quality_controlled":"1","publisher":"Elsevier","file":[{"date_created":"2022-08-02T10:37:55Z","relation":"main_file","content_type":"application/pdf","file_size":631391,"checksum":"63efcefaa1f2717244ef5407bd564426","date_updated":"2022-08-02T10:37:55Z","file_name":"2022_JourFunctionalAnalysis_Roos.pdf","file_id":"11720","access_level":"open_access","success":1,"creator":"dernst"}],"language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2022","oa":1,"issue":"12","doi":"10.1016/j.jfa.2022.109455","has_accepted_license":"1","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"14374"}]},"month":"06","isi":1,"arxiv":1,"acknowledgement":"We thank Rupert Frank for contributing Appendix B. Funding from the European Union's Horizon 2020 research and innovation programme under the ERC grant agreement No. 694227 is gratefully acknowledged.","type":"journal_article","keyword":["Analysis"],"volume":282,"status":"public","ec_funded":1,"publication_identifier":{"issn":["0022-1236"]}},{"type":"journal_article","acknowledgement":"We thank Suzanne Aigrain and Joe Llama for providing us with the simulated data used in Aigrain et al. (2015). S. N. B., L. B. and R. A. G. acknowledge the support from PLATO and GOLF CNES grants. A. R. G. S. acknowledges the support from NASA under grant NNX17AF27G. S. M. acknowledges the support from the Spanish Ministry of Science and Innovation with the Ramon y Cajal fellowship number RYC-2015-17697. P. L. P. and S. M. acknowledge support from the Spanish Ministry of Science and Innovation with the grant number PID2019-107187GB-I00. This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. Software: Python (Van Rossum & Drake 2009), numpy (Oliphant 2006), pandas (The pandas development team 2020; McKinney 2010), matplotlib (Hunter 2007), scikit-learn (Pedregosa et al. 2011). The source code used to obtain the present results can be found at: https://gitlab.com/sybreton/pushkin ; https://gitlab.com/sybreton/ml_surface_rotation_paper .","status":"public","publication_identifier":{"eissn":["1432-0746"],"issn":["0004-6361"]},"keyword":["Space and Planetary Science","Astronomy and Astrophysics","methods: data analysis / stars: solar-type / stars: activity / stars: rotation / starspots"],"volume":647,"doi":"10.1051/0004-6361/202039947","language":[{"iso":"eng"}],"year":"2021","extern":"1","oa":1,"arxiv":1,"month":"03","_id":"11608","oa_version":"Preprint","article_processing_charge":"No","day":"19","intvolume":"       647","scopus_import":"1","article_type":"original","publisher":"EDP Sciences","citation":{"ista":"Breton SN, Santos ARG, Bugnet LA, Mathur S, García RA, Pallé PL. 2021. ROOSTER: A machine-learning analysis tool for Kepler stellar rotation periods. Astronomy &#38; Astrophysics. 647, A125.","ieee":"S. N. Breton, A. R. G. Santos, L. A. Bugnet, S. Mathur, R. A. García, and P. L. Pallé, “ROOSTER: A machine-learning analysis tool for Kepler stellar rotation periods,” <i>Astronomy &#38; Astrophysics</i>, vol. 647. EDP Sciences, 2021.","mla":"Breton, S. N., et al. “ROOSTER: A Machine-Learning Analysis Tool for Kepler Stellar Rotation Periods.” <i>Astronomy &#38; Astrophysics</i>, vol. 647, A125, EDP Sciences, 2021, doi:<a href=\"https://doi.org/10.1051/0004-6361/202039947\">10.1051/0004-6361/202039947</a>.","short":"S.N. Breton, A.R.G. Santos, L.A. Bugnet, S. Mathur, R.A. García, P.L. Pallé, Astronomy &#38; Astrophysics 647 (2021).","apa":"Breton, S. N., Santos, A. R. G., Bugnet, L. A., Mathur, S., García, R. A., &#38; Pallé, P. L. (2021). ROOSTER: A machine-learning analysis tool for Kepler stellar rotation periods. <i>Astronomy &#38; Astrophysics</i>. EDP Sciences. <a href=\"https://doi.org/10.1051/0004-6361/202039947\">https://doi.org/10.1051/0004-6361/202039947</a>","ama":"Breton SN, Santos ARG, Bugnet LA, Mathur S, García RA, Pallé PL. ROOSTER: A machine-learning analysis tool for Kepler stellar rotation periods. <i>Astronomy &#38; Astrophysics</i>. 2021;647. doi:<a href=\"https://doi.org/10.1051/0004-6361/202039947\">10.1051/0004-6361/202039947</a>","chicago":"Breton, S. N., A. R. G. Santos, Lisa Annabelle Bugnet, S. Mathur, R. A. García, and P. L. Pallé. “ROOSTER: A Machine-Learning Analysis Tool for Kepler Stellar Rotation Periods.” <i>Astronomy &#38; Astrophysics</i>. EDP Sciences, 2021. <a href=\"https://doi.org/10.1051/0004-6361/202039947\">https://doi.org/10.1051/0004-6361/202039947</a>."},"quality_controlled":"1","article_number":"A125","date_published":"2021-03-19T00:00:00Z","publication":"Astronomy & Astrophysics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","abstract":[{"lang":"eng","text":"In order to understand stellar evolution, it is crucial to efficiently determine stellar surface rotation periods. Indeed, while they are of great importance in stellar models, angular momentum transport processes inside stars are still poorly understood today. Surface rotation, which is linked to the age of the star, is one of the constraints needed to improve the way those processes are modelled. Statistics of the surface rotation periods for a large sample of stars of different spectral types are thus necessary. An efficient tool to automatically determine reliable rotation periods is needed when dealing with large samples of stellar photometric datasets. The objective of this work is to develop such a tool. For this purpose, machine learning classifiers constitute relevant bases to build our new methodology. Random forest learning abilities are exploited to automate the extraction of rotation periods in Kepler light curves. Rotation periods and complementary parameters are obtained via three different methods: a wavelet analysis, the autocorrelation function of the light curve, and the composite spectrum. We trained three different classifiers: one to detect if rotational modulations are present in the light curve, one to flag close binary or classical pulsators candidates that can bias our rotation period determination, and finally one classifier to provide the final rotation period. We tested our machine learning pipeline on 23 431 stars of the Kepler K and M dwarf reference rotation catalogue for which 60% of the stars have been visually inspected. For the sample of 21 707 stars where all the input parameters are provided to the algorithm, 94.2% of them are correctly classified (as rotating or not). Among the stars that have a rotation period in the reference catalogue, the machine learning provides a period that agrees within 10% of the reference value for 95.3% of the stars. Moreover, the yield of correct rotation periods is raised to 99.5% after visually inspecting 25.2% of the stars. Over the two main analysis steps, rotation classification and period selection, the pipeline yields a global agreement with the reference values of 92.1% and 96.9% before and after visual inspection. Random forest classifiers are efficient tools to determine reliable rotation periods in large samples of stars. The methodology presented here could be easily adapted to extract surface rotation periods for stars with different spectral types or observed by other instruments such as K2, TESS or by PLATO in the near future."}],"date_updated":"2022-08-22T08:47:47Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2101.10152"}],"date_created":"2022-07-18T12:21:32Z","external_id":{"arxiv":["2101.10152"]},"title":"ROOSTER: A machine-learning analysis tool for Kepler stellar rotation periods","author":[{"first_name":"S. N.","last_name":"Breton","full_name":"Breton, S. N."},{"full_name":"Santos, A. R. G.","last_name":"Santos","first_name":"A. R. G."},{"orcid":"0000-0003-0142-4000","first_name":"Lisa Annabelle","last_name":"Bugnet","full_name":"Bugnet, Lisa Annabelle","id":"d9edb345-f866-11ec-9b37-d119b5234501"},{"full_name":"Mathur, S.","first_name":"S.","last_name":"Mathur"},{"full_name":"García, R. A.","last_name":"García","first_name":"R. A."},{"first_name":"P. L.","last_name":"Pallé","full_name":"Pallé, P. L."}]},{"month":"03","year":"2021","oa":1,"language":[{"iso":"eng"}],"issue":"6","doi":"10.1016/j.jfa.2020.108848","volume":280,"OA_place":"publisher","keyword":["Analysis"],"publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"status":"public","type":"journal_article","date_created":"2024-04-03T07:24:57Z","author":[{"first_name":"Daniel","last_name":"Lenz","full_name":"Lenz, Daniel"},{"last_name":"Schmidt","first_name":"Marcel","full_name":"Schmidt, Marcel"},{"id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","full_name":"Wirth, Melchior","orcid":"0000-0002-0519-4241","last_name":"Wirth","first_name":"Melchior"}],"title":"Uniqueness of form extensions and domination of semigroups","date_updated":"2025-06-25T07:41:05Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.jfa.2020.108848"}],"abstract":[{"text":"In this article, we study uniqueness of form extensions in a rather general setting. The method is based on the theory of ordered Hilbert spaces and the concept of domination of semigroups. Our main abstract result transfers uniqueness of form extension of a dominating form to that of a dominated form. This result can be applied to a multitude of examples including various magnetic Schrödinger forms on graphs and on manifolds.","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","publication":"Journal of Functional Analysis","OA_type":"free access","date_published":"2021-03-15T00:00:00Z","article_number":"108848","corr_author":"1","citation":{"ieee":"D. Lenz, M. Schmidt, and M. Wirth, “Uniqueness of form extensions and domination of semigroups,” <i>Journal of Functional Analysis</i>, vol. 280, no. 6. Elsevier, 2021.","mla":"Lenz, Daniel, et al. “Uniqueness of Form Extensions and Domination of Semigroups.” <i>Journal of Functional Analysis</i>, vol. 280, no. 6, 108848, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108848\">10.1016/j.jfa.2020.108848</a>.","short":"D. Lenz, M. Schmidt, M. Wirth, Journal of Functional Analysis 280 (2021).","ista":"Lenz D, Schmidt M, Wirth M. 2021. Uniqueness of form extensions and domination of semigroups. Journal of Functional Analysis. 280(6), 108848.","chicago":"Lenz, Daniel, Marcel Schmidt, and Melchior Wirth. “Uniqueness of Form Extensions and Domination of Semigroups.” <i>Journal of Functional Analysis</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.jfa.2020.108848\">https://doi.org/10.1016/j.jfa.2020.108848</a>.","ama":"Lenz D, Schmidt M, Wirth M. Uniqueness of form extensions and domination of semigroups. <i>Journal of Functional Analysis</i>. 2021;280(6). doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108848\">10.1016/j.jfa.2020.108848</a>","apa":"Lenz, D., Schmidt, M., &#38; Wirth, M. (2021). Uniqueness of form extensions and domination of semigroups. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2020.108848\">https://doi.org/10.1016/j.jfa.2020.108848</a>"},"quality_controlled":"1","publisher":"Elsevier","article_type":"original","scopus_import":"1","intvolume":"       280","department":[{"_id":"JaMa"}],"day":"15","_id":"15261","oa_version":"Published Version","article_processing_charge":"No"},{"arxiv":1,"isi":1,"month":"01","has_accepted_license":"1","page":"1-18","issue":"1","doi":"10.1515/agms-2020-0103","oa":1,"year":"2021","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"file":[{"file_id":"10857","access_level":"open_access","creator":"dernst","success":1,"date_created":"2022-03-18T09:31:59Z","relation":"main_file","date_updated":"2022-03-18T09:31:59Z","file_name":"2021_AnalysisMetricSpaces_Ivanov.pdf","file_size":789801,"content_type":"application/pdf","checksum":"7e615ac8489f5eae580b6517debfdc53"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2299-3274"]},"status":"public","volume":9,"keyword":["Applied Mathematics","Geometry and Topology","Analysis"],"type":"journal_article","acknowledgement":"The authors acknowledge the support of the grant of the Russian Government N 075-15-\r\n2019-1926. G.I.was supported also by the SwissNational Science Foundation grant 200021-179133. The authors are very grateful to the anonymous reviewer for valuable remarks.","date_updated":"2023-08-17T07:07:58Z","abstract":[{"text":"We study the properties of the maximal volume k-dimensional sections of the n-dimensional cube [−1, 1]n. We obtain a first order necessary condition for a k-dimensional subspace to be a local maximizer of the volume of such sections, which we formulate in a geometric way. We estimate the length of the projection of a vector of the standard basis of Rn onto a k-dimensional subspace that maximizes the volume of the intersection. We \u001cnd the optimal upper bound on the volume of a planar section of the cube [−1, 1]n , n ≥ 2.","lang":"eng"}],"author":[{"full_name":"Ivanov, Grigory","id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","last_name":"Ivanov","first_name":"Grigory"},{"full_name":"Tsiutsiurupa, Igor","last_name":"Tsiutsiurupa","first_name":"Igor"}],"title":"On the volume of sections of the cube","date_created":"2022-03-18T09:25:14Z","external_id":{"arxiv":["2004.02674"],"isi":["000734286800001"]},"date_published":"2021-01-29T00:00:00Z","publication_status":"published","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication":"Analysis and Geometry in Metric Spaces","file_date_updated":"2022-03-18T09:31:59Z","publisher":"De Gruyter","citation":{"chicago":"Ivanov, Grigory, and Igor Tsiutsiurupa. “On the Volume of Sections of the Cube.” <i>Analysis and Geometry in Metric Spaces</i>. De Gruyter, 2021. <a href=\"https://doi.org/10.1515/agms-2020-0103\">https://doi.org/10.1515/agms-2020-0103</a>.","apa":"Ivanov, G., &#38; Tsiutsiurupa, I. (2021). On the volume of sections of the cube. <i>Analysis and Geometry in Metric Spaces</i>. De Gruyter. <a href=\"https://doi.org/10.1515/agms-2020-0103\">https://doi.org/10.1515/agms-2020-0103</a>","ama":"Ivanov G, Tsiutsiurupa I. On the volume of sections of the cube. <i>Analysis and Geometry in Metric Spaces</i>. 2021;9(1):1-18. doi:<a href=\"https://doi.org/10.1515/agms-2020-0103\">10.1515/agms-2020-0103</a>","short":"G. Ivanov, I. Tsiutsiurupa, Analysis and Geometry in Metric Spaces 9 (2021) 1–18.","mla":"Ivanov, Grigory, and Igor Tsiutsiurupa. “On the Volume of Sections of the Cube.” <i>Analysis and Geometry in Metric Spaces</i>, vol. 9, no. 1, De Gruyter, 2021, pp. 1–18, doi:<a href=\"https://doi.org/10.1515/agms-2020-0103\">10.1515/agms-2020-0103</a>.","ieee":"G. Ivanov and I. Tsiutsiurupa, “On the volume of sections of the cube,” <i>Analysis and Geometry in Metric Spaces</i>, vol. 9, no. 1. De Gruyter, pp. 1–18, 2021.","ista":"Ivanov G, Tsiutsiurupa I. 2021. On the volume of sections of the cube. Analysis and Geometry in Metric Spaces. 9(1), 1–18."},"quality_controlled":"1","ddc":["510"],"day":"29","oa_version":"Published Version","article_processing_charge":"No","_id":"10856","article_type":"original","scopus_import":"1","department":[{"_id":"UlWa"}],"intvolume":"         9"},{"external_id":{"isi":["000668431200001"],"arxiv":["1908.02273"]},"date_created":"2021-12-16T12:12:33Z","author":[{"id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87","full_name":"Fischer, Julian L","last_name":"Fischer","first_name":"Julian L","orcid":"0000-0002-0479-558X"},{"full_name":"Neukamm, Stefan","last_name":"Neukamm","first_name":"Stefan"}],"title":"Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems","date_updated":"2023-08-17T06:23:21Z","abstract":[{"text":"We derive optimal-order homogenization rates for random nonlinear elliptic PDEs with monotone nonlinearity in the uniformly elliptic case. More precisely, for a random monotone operator on \\mathbb {R}^d with stationary law (that is spatially homogeneous statistics) and fast decay of correlations on scales larger than the microscale \\varepsilon >0, we establish homogenization error estimates of the order \\varepsilon in case d\\geqq 3, and of the order \\varepsilon |\\log \\varepsilon |^{1/2} in case d=2. Previous results in nonlinear stochastic homogenization have been limited to a small algebraic rate of convergence \\varepsilon ^\\delta . We also establish error estimates for the approximation of the homogenized operator by the method of representative volumes of the order (L/\\varepsilon )^{-d/2} for a representative volume of size L. Our results also hold in the case of systems for which a (small-scale) C^{1,\\alpha } regularity theory is available.","lang":"eng"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","file_date_updated":"2021-12-16T14:58:08Z","publication":"Archive for Rational Mechanics and Analysis","date_published":"2021-06-30T00:00:00Z","citation":{"chicago":"Fischer, Julian L, and Stefan Neukamm. “Optimal Homogenization Rates in Stochastic Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00205-021-01686-9\">https://doi.org/10.1007/s00205-021-01686-9</a>.","ama":"Fischer JL, Neukamm S. Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems. <i>Archive for Rational Mechanics and Analysis</i>. 2021;242(1):343-452. doi:<a href=\"https://doi.org/10.1007/s00205-021-01686-9\">10.1007/s00205-021-01686-9</a>","apa":"Fischer, J. L., &#38; Neukamm, S. (2021). Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-021-01686-9\">https://doi.org/10.1007/s00205-021-01686-9</a>","ieee":"J. L. Fischer and S. Neukamm, “Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 242, no. 1. Springer Nature, pp. 343–452, 2021.","mla":"Fischer, Julian L., and Stefan Neukamm. “Optimal Homogenization Rates in Stochastic Homogenization of Nonlinear Uniformly Elliptic Equations and Systems.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 242, no. 1, Springer Nature, 2021, pp. 343–452, doi:<a href=\"https://doi.org/10.1007/s00205-021-01686-9\">10.1007/s00205-021-01686-9</a>.","short":"J.L. Fischer, S. Neukamm, Archive for Rational Mechanics and Analysis 242 (2021) 343–452.","ista":"Fischer JL, Neukamm S. 2021. Optimal homogenization rates in stochastic homogenization of nonlinear uniformly elliptic equations and systems. Archive for Rational Mechanics and Analysis. 242(1), 343–452."},"quality_controlled":"1","ddc":["530"],"publisher":"Springer Nature","scopus_import":"1","article_type":"original","intvolume":"       242","department":[{"_id":"JuFi"}],"day":"30","_id":"10549","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","month":"06","isi":1,"arxiv":1,"year":"2021","oa":1,"file":[{"file_id":"10558","access_level":"open_access","creator":"cchlebak","success":1,"date_created":"2021-12-16T14:58:08Z","relation":"main_file","file_name":"2021_ArchRatMechAnalysis_Fischer.pdf","date_updated":"2021-12-16T14:58:08Z","content_type":"application/pdf","checksum":"cc830b739aed83ca2e32c4e0ce266a4c","file_size":1640121}],"language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"issue":"1","doi":"10.1007/s00205-021-01686-9","has_accepted_license":"1","page":"343-452","volume":242,"keyword":["Mechanical Engineering","Mathematics (miscellaneous)","Analysis"],"publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"status":"public","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). SN acknowledges partial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – project number 405009441.","type":"journal_article"},{"citation":{"ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Spectral rigidity for addition of random matrices at the regular edge,” <i>Journal of Functional Analysis</i>, vol. 279, no. 7. Elsevier, 2020.","short":"Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 279 (2020).","mla":"Bao, Zhigang, et al. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” <i>Journal of Functional Analysis</i>, vol. 279, no. 7, 108639, Elsevier, 2020, doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">10.1016/j.jfa.2020.108639</a>.","ista":"Bao Z, Erdös L, Schnelli K. 2020. Spectral rigidity for addition of random matrices at the regular edge. Journal of Functional Analysis. 279(7), 108639.","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” <i>Journal of Functional Analysis</i>. Elsevier, 2020. <a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">https://doi.org/10.1016/j.jfa.2020.108639</a>.","ama":"Bao Z, Erdös L, Schnelli K. Spectral rigidity for addition of random matrices at the regular edge. <i>Journal of Functional Analysis</i>. 2020;279(7). doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">10.1016/j.jfa.2020.108639</a>","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2020). Spectral rigidity for addition of random matrices at the regular edge. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">https://doi.org/10.1016/j.jfa.2020.108639</a>"},"quality_controlled":"1","publisher":"Elsevier","intvolume":"       279","department":[{"_id":"LaEr"}],"scopus_import":"1","article_type":"original","_id":"10862","article_processing_charge":"No","oa_version":"Preprint","day":"15","external_id":{"arxiv":["1708.01597"],"isi":["000559623200009"]},"date_created":"2022-03-18T10:18:59Z","title":"Spectral rigidity for addition of random matrices at the regular edge","author":[{"full_name":"Bao, Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","first_name":"Zhigang","last_name":"Bao","orcid":"0000-0003-3036-1475"},{"orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Schnelli, Kevin","last_name":"Schnelli","first_name":"Kevin"}],"project":[{"call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"abstract":[{"text":"We consider the sum of two large Hermitian matrices A and B with a Haar unitary conjugation bringing them into a general relative position. We prove that the eigenvalue density on the scale slightly above the local eigenvalue spacing is asymptotically given by the free additive convolution of the laws of A and B as the dimension of the matrix increases. This implies optimal rigidity of the eigenvalues and optimal rate of convergence in Voiculescu's theorem. Our previous works [4], [5] established these results in the bulk spectrum, the current paper completely settles the problem at the spectral edges provided they have the typical square-root behavior. The key element of our proof is to compensate the deterioration of the stability of the subordination equations by sharp error estimates that properly account for the local density near the edge. Our results also hold if the Haar unitary matrix is replaced by the Haar orthogonal matrix.","lang":"eng"}],"date_updated":"2025-04-15T08:05:01Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.01597"}],"publication":"Journal of Functional Analysis","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","article_number":"108639","corr_author":"1","date_published":"2020-10-15T00:00:00Z","keyword":["Analysis"],"volume":279,"status":"public","ec_funded":1,"publication_identifier":{"issn":["0022-1236"]},"acknowledgement":"Partially supported by ERC Advanced Grant RANMAT No. 338804.","type":"journal_article","month":"10","isi":1,"arxiv":1,"language":[{"iso":"eng"}],"year":"2020","oa":1,"doi":"10.1016/j.jfa.2020.108639","issue":"7"}]