[{"year":"2023","type":"journal_article","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"ec_funded":1,"day":"01","issue":"4","corr_author":"1","month":"08","publisher":"Institute of Mathematical Statistics","date_updated":"2025-09-09T14:12:00Z","language":[{"iso":"eng"}],"publication":"The Annals of Applied Probability","department":[{"_id":"LaEr"}],"isi":1,"article_processing_charge":"No","status":"public","external_id":{"isi":["001031710500012"],"arxiv":["2010.16083"]},"publication_identifier":{"issn":["1050-5164"]},"volume":33,"article_type":"original","intvolume":"        33","acknowledgement":"The first author is partially supported by NSF Grant DMS-2113489 and grateful for the AMS-SIMONS travel grant (2020–2023). The second author is supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nThe authors would like to thank the Editor, Associate Editor and an anonymous referee for their many critical suggestions which have significantly improved the paper. We also want to thank Zhigang Bao and Ji Oon Lee for many helpful discussions and comments.","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_published":"2023-08-01T00:00:00Z","oa":1,"arxiv":1,"citation":{"apa":"Ding, X., &#38; Ji, H. C. (2023). Local laws for multiplication of random matrices. <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-aap1882\">https://doi.org/10.1214/22-aap1882</a>","short":"X. Ding, H.C. Ji, The Annals of Applied Probability 33 (2023) 2981–3009.","mla":"Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random Matrices.” <i>The Annals of Applied Probability</i>, vol. 33, no. 4, Institute of Mathematical Statistics, 2023, pp. 2981–3009, doi:<a href=\"https://doi.org/10.1214/22-aap1882\">10.1214/22-aap1882</a>.","chicago":"Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random Matrices.” <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/22-aap1882\">https://doi.org/10.1214/22-aap1882</a>.","ama":"Ding X, Ji HC. Local laws for multiplication of random matrices. <i>The Annals of Applied Probability</i>. 2023;33(4):2981-3009. doi:<a href=\"https://doi.org/10.1214/22-aap1882\">10.1214/22-aap1882</a>","ieee":"X. Ding and H. C. Ji, “Local laws for multiplication of random matrices,” <i>The Annals of Applied Probability</i>, vol. 33, no. 4. Institute of Mathematical Statistics, pp. 2981–3009, 2023.","ista":"Ding X, Ji HC. 2023. Local laws for multiplication of random matrices. The Annals of Applied Probability. 33(4), 2981–3009."},"_id":"14750","scopus_import":"1","date_created":"2024-01-08T13:03:18Z","author":[{"full_name":"Ding, Xiucai","first_name":"Xiucai","last_name":"Ding"},{"last_name":"Ji","first_name":"Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","full_name":"Ji, Hong Chang"}],"doi":"10.1214/22-aap1882","oa_version":"Preprint","title":"Local laws for multiplication of random matrices","publication_status":"published","abstract":[{"lang":"eng","text":"Consider the random matrix model A1/2UBU∗A1/2, where A and B are two N × N deterministic matrices and U is either an N × N Haar unitary or orthogonal random matrix. It is well known that on the macroscopic scale (Invent. Math. 104 (1991) 201–220), the limiting empirical spectral distribution (ESD) of the above model is given by the free multiplicative convolution\r\nof the limiting ESDs of A and B, denoted as μα \u0002 μβ, where μα and μβ are the limiting ESDs of A and B, respectively. In this paper, we study the asymptotic microscopic behavior of the edge eigenvalues and eigenvectors statistics. We prove that both the density of μA \u0002μB, where μA and μB are the ESDs of A and B, respectively and the associated subordination functions\r\nhave a regular behavior near the edges. Moreover, we establish the local laws near the edges on the optimal scale. In particular, we prove that the entries of the resolvent are close to some functionals depending only on the eigenvalues of A, B and the subordination functions with optimal convergence rates. Our proofs and calculations are based on the techniques developed for the additive model A+UBU∗ in (J. Funct. Anal. 271 (2016) 672–719; Comm. Math.\r\nPhys. 349 (2017) 947–990; Adv. Math. 319 (2017) 251–291; J. Funct. Anal. 279 (2020) 108639), and our results can be regarded as the counterparts of (J. Funct. Anal. 279 (2020) 108639) for the multiplicative model. "}],"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2010.16083"}],"page":"2981-3009"},{"publication_status":"published","oa_version":"Preprint","title":"Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices","abstract":[{"lang":"eng","text":"We establish a quantitative version of the Tracy–Widom law for the largest eigenvalue of high-dimensional sample covariance matrices. To be precise, we show that the fluctuations of the largest eigenvalue of a sample covariance matrix X∗X converge to its Tracy–Widom limit at a rate nearly N−1/3, where X is an M×N random matrix whose entries are independent real or complex random variables, assuming that both M and N tend to infinity at a constant rate. This result improves the previous estimate N−2/9 obtained by Wang (2019). Our proof relies on a Green function comparison method (Adv. Math. 229 (2012) 1435–1515) using iterative cumulant expansions, the local laws for the Green function and asymptotic properties of the correlation kernel of the white Wishart ensemble."}],"quality_controlled":"1","page":"677-725","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2108.02728"}],"article_type":"original","publication_identifier":{"issn":["1050-5164"]},"volume":33,"acknowledgement":"K. Schnelli was supported by the Swedish Research Council Grants VR-2017-05195, and the Knut and Alice Wallenberg Foundation. Y. Xu was supported by the Swedish Research Council Grant VR-2017-05195 and the ERC Advanced Grant “RMTBeyond” No. 101020331.","intvolume":"        33","arxiv":1,"citation":{"apa":"Schnelli, K., &#38; Xu, Y. (2023). Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-aap1826\">https://doi.org/10.1214/22-aap1826</a>","mla":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Sample Covariance Matrices.” <i>The Annals of Applied Probability</i>, vol. 33, no. 1, Institute of Mathematical Statistics, 2023, pp. 677–725, doi:<a href=\"https://doi.org/10.1214/22-aap1826\">10.1214/22-aap1826</a>.","chicago":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Sample Covariance Matrices.” <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/22-aap1826\">https://doi.org/10.1214/22-aap1826</a>.","short":"K. Schnelli, Y. Xu, The Annals of Applied Probability 33 (2023) 677–725.","ama":"Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. <i>The Annals of Applied Probability</i>. 2023;33(1):677-725. doi:<a href=\"https://doi.org/10.1214/22-aap1826\">10.1214/22-aap1826</a>","ieee":"K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices,” <i>The Annals of Applied Probability</i>, vol. 33, no. 1. Institute of Mathematical Statistics, pp. 677–725, 2023.","ista":"Schnelli K, Xu Y. 2023. Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. The Annals of Applied Probability. 33(1), 677–725."},"oa":1,"date_published":"2023-02-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2024-01-10T09:23:31Z","author":[{"full_name":"Schnelli, Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin","last_name":"Schnelli","orcid":"0000-0003-0954-3231"},{"full_name":"Xu, Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","first_name":"Yuanyuan","orcid":"0000-0003-1559-1205","last_name":"Xu"}],"doi":"10.1214/22-aap1826","scopus_import":"1","_id":"14775","date_updated":"2025-04-14T07:57:19Z","language":[{"iso":"eng"}],"article_processing_charge":"No","department":[{"_id":"LaEr"}],"isi":1,"publication":"The Annals of Applied Probability","external_id":{"isi":["000946432400021"],"arxiv":["2108.02728"]},"status":"public","type":"journal_article","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"year":"2023","ec_funded":1,"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"day":"01","issue":"1","publisher":"Institute of Mathematical Statistics","month":"02","corr_author":"1"},{"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","arxiv":1,"citation":{"mla":"Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and Principal Components.” <i>Stochastic Processes and Their Applications</i>, vol. 163, Elsevier, 2023, pp. 25–60, doi:<a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">10.1016/j.spa.2023.05.009</a>.","chicago":"Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and Principal Components.” <i>Stochastic Processes and Their Applications</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">https://doi.org/10.1016/j.spa.2023.05.009</a>.","short":"X. Ding, H.C. Ji, Stochastic Processes and Their Applications 163 (2023) 25–60.","ama":"Ding X, Ji HC. Spiked multiplicative random matrices and principal components. <i>Stochastic Processes and their Applications</i>. 2023;163:25-60. doi:<a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">10.1016/j.spa.2023.05.009</a>","apa":"Ding, X., &#38; Ji, H. C. (2023). Spiked multiplicative random matrices and principal components. <i>Stochastic Processes and Their Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">https://doi.org/10.1016/j.spa.2023.05.009</a>","ista":"Ding X, Ji HC. 2023. Spiked multiplicative random matrices and principal components. Stochastic Processes and their Applications. 163, 25–60.","ieee":"X. Ding and H. C. Ji, “Spiked multiplicative random matrices and principal components,” <i>Stochastic Processes and their Applications</i>, vol. 163. Elsevier, pp. 25–60, 2023."},"oa":1,"date_published":"2023-09-01T00:00:00Z","scopus_import":"1","_id":"14780","author":[{"full_name":"Ding, Xiucai","last_name":"Ding","first_name":"Xiucai"},{"last_name":"Ji","first_name":"Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","full_name":"Ji, Hong Chang"}],"doi":"10.1016/j.spa.2023.05.009","date_created":"2024-01-10T09:29:25Z","article_type":"original","publication_identifier":{"eissn":["1879-209X"],"issn":["0304-4149"]},"volume":163,"acknowledgement":"The authors would like to thank the editor, the associated editor and two anonymous referees for their many critical suggestions which have significantly improved the paper. The authors are also grateful to Zhigang Bao and Ji Oon Lee for many helpful discussions. The first author also wants to thank Hari Bercovici for many useful comments. The first author is partially supported by National Science Foundation DMS-2113489 and the second author is supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","intvolume":"       163","file_date_updated":"2024-01-16T08:47:31Z","quality_controlled":"1","page":"25-60","title":"Spiked multiplicative random matrices and principal components","oa_version":"Published Version","publication_status":"published","abstract":[{"text":"In this paper, we study the eigenvalues and eigenvectors of the spiked invariant multiplicative models when the randomness is from Haar matrices. We establish the limits of the outlier eigenvalues λˆi and the generalized components (⟨v,uˆi⟩ for any deterministic vector v) of the outlier eigenvectors uˆi with optimal convergence rates. Moreover, we prove that the non-outlier eigenvalues stick with those of the unspiked matrices and the non-outlier eigenvectors are delocalized. The results also hold near the so-called BBP transition and for degenerate spikes. On one hand, our results can be regarded as a refinement of the counterparts of [12] under additional regularity conditions. On the other hand, they can be viewed as an analog of [34] by replacing the random matrix with i.i.d. entries with Haar random matrix.","lang":"eng"}],"license":"https://creativecommons.org/licenses/by/4.0/","day":"01","month":"09","publisher":"Elsevier","year":"2023","type":"journal_article","project":[{"grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"keyword":["Applied Mathematics","Modeling and Simulation","Statistics and Probability"],"ec_funded":1,"department":[{"_id":"LaEr"}],"isi":1,"has_accepted_license":"1","publication":"Stochastic Processes and their Applications","article_processing_charge":"Yes (in subscription journal)","status":"public","external_id":{"arxiv":["2302.13502"],"isi":["001113615900001"]},"ddc":["510"],"date_updated":"2025-07-16T08:01:03Z","file":[{"relation":"main_file","creator":"dernst","access_level":"open_access","date_created":"2024-01-16T08:47:31Z","checksum":"46a708b0cd5569a73d0f3d6c3e0a44dc","file_id":"14806","file_name":"2023_StochasticProcAppl_Ding.pdf","success":1,"date_updated":"2024-01-16T08:47:31Z","file_size":1870349,"content_type":"application/pdf"}],"language":[{"iso":"eng"}]},{"scopus_import":"1","_id":"14849","author":[{"orcid":"0000-0002-4901-7992","last_name":"Cipolloni","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","first_name":"Dominik J"},{"first_name":"Yuanyuan","last_name":"Xu","full_name":"Xu, Yuanyuan"}],"date_created":"2024-01-22T08:08:41Z","doi":"10.1214/23-aop1643","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2023. On the rightmost eigenvalue of non-Hermitian random matrices. The Annals of Probability. 51(6), 2192–2242.","ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “On the rightmost eigenvalue of non-Hermitian random matrices,” <i>The Annals of Probability</i>, vol. 51, no. 6. Institute of Mathematical Statistics, pp. 2192–2242, 2023.","chicago":"Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/23-aop1643\">https://doi.org/10.1214/23-aop1643</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, The Annals of Probability 51 (2023) 2192–2242.","mla":"Cipolloni, Giorgio, et al. “On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>, vol. 51, no. 6, Institute of Mathematical Statistics, 2023, pp. 2192–242, doi:<a href=\"https://doi.org/10.1214/23-aop1643\">10.1214/23-aop1643</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. On the rightmost eigenvalue of non-Hermitian random matrices. <i>The Annals of Probability</i>. 2023;51(6):2192-2242. doi:<a href=\"https://doi.org/10.1214/23-aop1643\">10.1214/23-aop1643</a>","apa":"Cipolloni, G., Erdös, L., Schröder, D. J., &#38; Xu, Y. (2023). On the rightmost eigenvalue of non-Hermitian random matrices. <i>The Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-aop1643\">https://doi.org/10.1214/23-aop1643</a>"},"arxiv":1,"oa":1,"date_published":"2023-11-01T00:00:00Z","acknowledgement":"The second and the fourth author were supported by the ERC Advanced Grant\r\n“RMTBeyond” No. 101020331. The third author was supported by Dr. Max Rössler, the\r\nWalter Haefner Foundation and the ETH Zürich Foundation.","intvolume":"        51","article_type":"original","publication_identifier":{"issn":["0091-1798"]},"volume":51,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2206.04448"}],"page":"2192-2242","quality_controlled":"1","abstract":[{"text":"We establish a precise three-term asymptotic expansion, with an optimal estimate of the error term, for the rightmost eigenvalue of an n×n random matrix with independent identically distributed complex entries as n tends to infinity. All terms in the expansion are universal.","lang":"eng"}],"title":"On the rightmost eigenvalue of non-Hermitian random matrices","oa_version":"Preprint","publication_status":"published","month":"11","corr_author":"1","publisher":"Institute of Mathematical Statistics","day":"01","issue":"6","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"ec_funded":1,"year":"2023","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"type":"journal_article","status":"public","external_id":{"arxiv":["2206.04448"],"isi":["001112165000004"]},"isi":1,"department":[{"_id":"LaEr"}],"publication":"The Annals of Probability","article_processing_charge":"No","language":[{"iso":"eng"}],"date_updated":"2025-09-09T14:23:34Z"},{"page":"946-1034","quality_controlled":"1","file_date_updated":"2023-10-04T09:21:48Z","abstract":[{"lang":"eng","text":"We consider large non-Hermitian random matrices X with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are asymptotically Gaussian for test functions having 2+ϵ derivatives. Previously this result was known only for a few special cases; either the test functions were required to be analytic [72], or the distribution of the matrix elements needed to be Gaussian [73], or at least match the Gaussian up to the first four moments [82, 56]. We find the exact dependence of the limiting variance on the fourth cumulant that was not known before. The proof relies on two novel ingredients: (i) a local law for a product of two resolvents of the Hermitisation of X with different spectral parameters and (ii) a coupling of several weakly dependent Dyson Brownian motions. These methods are also the key inputs for our analogous results on the linear eigenvalue statistics of real matrices X that are presented in the companion paper [32]. "}],"oa_version":"Published Version","title":"Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices","publication_status":"published","scopus_import":"1","_id":"10405","date_created":"2021-12-05T23:01:41Z","author":[{"orcid":"0000-0002-4901-7992","last_name":"Cipolloni","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"doi":"10.1002/cpa.22028","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. 76(5), 946–1034.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices,” <i>Communications on Pure and Applied Mathematics</i>, vol. 76, no. 5. Wiley, pp. 946–1034, 2023.","ama":"Cipolloni G, Erdös L, Schröder DJ. Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. 2023;76(5):946-1034. doi:<a href=\"https://doi.org/10.1002/cpa.22028\">10.1002/cpa.22028</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Central Limit Theorem for Linear Eigenvalue Statistics of Non-Hermitian Random Matrices.” <i>Communications on Pure and Applied Mathematics</i>. Wiley, 2023. <a href=\"https://doi.org/10.1002/cpa.22028\">https://doi.org/10.1002/cpa.22028</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications on Pure and Applied Mathematics 76 (2023) 946–1034.","mla":"Cipolloni, Giorgio, et al. “Central Limit Theorem for Linear Eigenvalue Statistics of Non-Hermitian Random Matrices.” <i>Communications on Pure and Applied Mathematics</i>, vol. 76, no. 5, Wiley, 2023, pp. 946–1034, doi:<a href=\"https://doi.org/10.1002/cpa.22028\">10.1002/cpa.22028</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. Wiley. <a href=\"https://doi.org/10.1002/cpa.22028\">https://doi.org/10.1002/cpa.22028</a>"},"oa":1,"date_published":"2023-05-01T00:00:00Z","acknowledgement":"L.E. would like to thank Nathanaël Berestycki and D.S.would like to thank Nina Holden for valuable discussions on the Gaussian freefield.G.C. and L.E. are partially supported by ERC Advanced Grant No. 338804.G.C. received funding from the European Union’s Horizon 2020 research and in-novation programme under the Marie Skłodowska-Curie Grant Agreement No.665385. D.S. is supported by Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation.","intvolume":"        76","article_type":"original","volume":76,"publication_identifier":{"issn":["0010-3640"],"eissn":["1097-0312"]},"status":"public","external_id":{"arxiv":["1912.04100"],"isi":["000724652500001"]},"department":[{"_id":"LaEr"}],"has_accepted_license":"1","isi":1,"publication":"Communications on Pure and Applied Mathematics","article_processing_charge":"Yes (via OA deal)","language":[{"iso":"eng"}],"date_updated":"2025-03-31T16:00:54Z","file":[{"success":1,"file_size":803440,"date_updated":"2023-10-04T09:21:48Z","content_type":"application/pdf","creator":"dernst","access_level":"open_access","checksum":"8346bc2642afb4ccb7f38979f41df5d9","date_created":"2023-10-04T09:21:48Z","file_name":"2023_CommPureMathematics_Cipolloni.pdf","file_id":"14388","relation":"main_file"}],"ddc":["510"],"month":"05","corr_author":"1","publisher":"Wiley","license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","issue":"5","day":"01","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)"},"ec_funded":1,"year":"2023","type":"journal_article","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","call_identifier":"H2020","name":"International IST Doctoral Program"}]},{"year":"2023","type":"journal_article","issue":"01","day":"01","month":"01","publisher":"World Scientific Publishing","date_updated":"2025-09-09T14:27:10Z","language":[{"iso":"eng"}],"isi":1,"department":[{"_id":"LaEr"}],"publication":"Random Matrices: Theory and Applications","article_processing_charge":"No","status":"public","article_number":"2250049","external_id":{"isi":["000848874400001"],"arxiv":["2109.10331"]},"article_type":"original","publication_identifier":{"eissn":["2010-3271"],"issn":["2010-3263"]},"volume":12,"acknowledgement":"N.S. gratefully acknowledges financial support of the Royal Society, grant URF/R1/180707. We would like to thank Emma Bailey, Yan Fyodorov and Jordan Stoyanov for helpful comments an an earlier version of this paper. We are grateful for the comments of an anonymous referee.","intvolume":"        12","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","citation":{"ista":"Serebryakov A, Simm N, Dubach G. 2023. Characteristic polynomials of random truncations: Moments, duality and asymptotics. Random Matrices: Theory and Applications. 12(01), 2250049.","ieee":"A. Serebryakov, N. Simm, and G. Dubach, “Characteristic polynomials of random truncations: Moments, duality and asymptotics,” <i>Random Matrices: Theory and Applications</i>, vol. 12, no. 01. World Scientific Publishing, 2023.","ama":"Serebryakov A, Simm N, Dubach G. Characteristic polynomials of random truncations: Moments, duality and asymptotics. <i>Random Matrices: Theory and Applications</i>. 2023;12(01). doi:<a href=\"https://doi.org/10.1142/s2010326322500496\">10.1142/s2010326322500496</a>","chicago":"Serebryakov, Alexander, Nick Simm, and Guillaume Dubach. “Characteristic Polynomials of Random Truncations: Moments, Duality and Asymptotics.” <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing, 2023. <a href=\"https://doi.org/10.1142/s2010326322500496\">https://doi.org/10.1142/s2010326322500496</a>.","mla":"Serebryakov, Alexander, et al. “Characteristic Polynomials of Random Truncations: Moments, Duality and Asymptotics.” <i>Random Matrices: Theory and Applications</i>, vol. 12, no. 01, 2250049, World Scientific Publishing, 2023, doi:<a href=\"https://doi.org/10.1142/s2010326322500496\">10.1142/s2010326322500496</a>.","short":"A. Serebryakov, N. Simm, G. Dubach, Random Matrices: Theory and Applications 12 (2023).","apa":"Serebryakov, A., Simm, N., &#38; Dubach, G. (2023). Characteristic polynomials of random truncations: Moments, duality and asymptotics. <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s2010326322500496\">https://doi.org/10.1142/s2010326322500496</a>"},"arxiv":1,"oa":1,"date_published":"2023-01-01T00:00:00Z","scopus_import":"1","_id":"17079","doi":"10.1142/s2010326322500496","date_created":"2024-05-29T06:14:26Z","author":[{"full_name":"Serebryakov, Alexander","first_name":"Alexander","last_name":"Serebryakov"},{"first_name":"Nick","last_name":"Simm","full_name":"Simm, Nick"},{"first_name":"Guillaume","last_name":"Dubach","orcid":"0000-0001-6892-8137","full_name":"Dubach, Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E"}],"title":"Characteristic polynomials of random truncations: Moments, duality and asymptotics","oa_version":"Preprint","publication_status":"published","abstract":[{"text":"We study moments of characteristic polynomials of truncated Haar distributed matrices from the three classical compact groups O(N), U(N) and Sp(2N). For finite matrix size we calculate the moments in terms of hypergeometric functions of matrix argument and give explicit integral representations highlighting the duality between the moment and the matrix size as well as the duality between the orthogonal and symplectic cases. Asymptotic expansions in strong and weak non-unitarity regimes are obtained. Using the connection to matrix hypergeometric functions, we establish limit theorems for the log-modulus of the characteristic polynomial evaluated on the unit circle.","lang":"eng"}],"quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2109.10331","open_access":"1"}]},{"file_date_updated":"2023-10-16T07:07:24Z","quality_controlled":"1","title":"Creation rate of Dirac particles at a point source","oa_version":"Published Version","publication_status":"published","abstract":[{"text":"Only recently has it been possible to construct a self-adjoint Hamiltonian that involves the creation of Dirac particles at a point source in 3d space. Its definition makes use of an interior-boundary condition. Here, we develop for this Hamiltonian a corresponding theory of the Bohmian configuration. That is, we (non-rigorously) construct a Markov jump process $(Q_t)_{t\\in\\mathbb{R}}$ in the configuration space of a variable number of particles that is $|\\psi_t|^2$-distributed at every time t and follows Bohmian trajectories between the jumps. The jumps correspond to particle creation or annihilation events and occur either to or from a configuration with a particle located at the source. The process is the natural analog of Bell's jump process, and a central piece in its construction is the determination of the rate of particle creation. The construction requires an analysis of the asymptotic behavior of the Bohmian trajectories near the source. We find that the particle reaches the source with radial speed 0, but orbits around the source infinitely many times in finite time before absorption (or after emission).","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2023-10-11T00:00:00Z","oa":1,"citation":{"ieee":"S. J. Henheik and R. Tumulka, “Creation rate of Dirac particles at a point source,” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 56, no. 44. IOP Publishing, 2023.","ista":"Henheik SJ, Tumulka R. 2023. Creation rate of Dirac particles at a point source. Journal of Physics A: Mathematical and Theoretical. 56(44), 445201.","apa":"Henheik, S. J., &#38; Tumulka, R. (2023). Creation rate of Dirac particles at a point source. <i>Journal of Physics A: Mathematical and Theoretical</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1751-8121/acfe62\">https://doi.org/10.1088/1751-8121/acfe62</a>","ama":"Henheik SJ, Tumulka R. Creation rate of Dirac particles at a point source. <i>Journal of Physics A: Mathematical and Theoretical</i>. 2023;56(44). doi:<a href=\"https://doi.org/10.1088/1751-8121/acfe62\">10.1088/1751-8121/acfe62</a>","short":"S.J. Henheik, R. Tumulka, Journal of Physics A: Mathematical and Theoretical 56 (2023).","mla":"Henheik, Sven Joscha, and Roderich Tumulka. “Creation Rate of Dirac Particles at a Point Source.” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 56, no. 44, 445201, IOP Publishing, 2023, doi:<a href=\"https://doi.org/10.1088/1751-8121/acfe62\">10.1088/1751-8121/acfe62</a>.","chicago":"Henheik, Sven Joscha, and Roderich Tumulka. “Creation Rate of Dirac Particles at a Point Source.” <i>Journal of Physics A: Mathematical and Theoretical</i>. IOP Publishing, 2023. <a href=\"https://doi.org/10.1088/1751-8121/acfe62\">https://doi.org/10.1088/1751-8121/acfe62</a>."},"arxiv":1,"_id":"14421","scopus_import":"1","date_created":"2023-10-12T12:42:53Z","doi":"10.1088/1751-8121/acfe62","author":[{"full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik"},{"full_name":"Tumulka, Roderich","first_name":"Roderich","last_name":"Tumulka"}],"publication_identifier":{"eissn":["1751-8121"],"issn":["1751-8113"]},"volume":56,"article_type":"original","intvolume":"        56","acknowledgement":"J H gratefully acknowledges partial financial support by the ERC Advanced Grant 'RMTBeyond' No. 101020331.","publication":"Journal of Physics A: Mathematical and Theoretical","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"isi":1,"has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","status":"public","external_id":{"arxiv":["2211.16606"],"isi":["001080908000001"]},"article_number":"445201","file":[{"relation":"main_file","file_name":"2023_JourPhysics_Henheik.pdf","checksum":"5b68de147dd4c608b71a6e0e844d2ce9","date_created":"2023-10-16T07:07:24Z","file_id":"14429","creator":"dernst","access_level":"open_access","content_type":"application/pdf","file_size":721399,"date_updated":"2023-10-16T07:07:24Z","success":1}],"date_updated":"2026-04-07T12:37:10Z","ddc":["510"],"related_material":{"record":[{"id":"19540","status":"public","relation":"dissertation_contains"}]},"language":[{"iso":"eng"}],"day":"11","issue":"44","corr_author":"1","month":"10","publisher":"IOP Publishing","year":"2023","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"type":"journal_article","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"ec_funded":1},{"abstract":[{"text":"We prove the Eigenstate Thermalisation Hypothesis (ETH) for local observables in a typical translation invariant system of quantum spins with L-body interactions, where L is the number of spins. This mathematically verifies the observation first made by Santos and Rigol (Phys Rev E 82(3):031130, 2010, https://doi.org/10.1103/PhysRevE.82.031130) that the ETH may hold for systems with additional translational symmetries for a naturally restricted class of observables. We also present numerical support for the same phenomenon for Hamiltonians with local interaction.","lang":"eng"}],"publication_status":"published","oa_version":"Published Version","title":"Eigenstate thermalisation hypothesis for translation invariant spin systems","quality_controlled":"1","file_date_updated":"2023-07-31T07:49:31Z","intvolume":"       190","acknowledgement":"LE, JH, and VR were supported by ERC Advanced Grant “RMTBeyond” No. 101020331. SS was supported by KAKENHI Grant Number JP22J14935 from the Japan Society for the Promotion of Science (JSPS) and Forefront Physics and Mathematics Program to Drive Transformation (FoPM), a World-leading Innovative Graduate Study (WINGS) Program, the University of Tokyo.\r\nOpen access funding provided by The University of Tokyo.","publication_identifier":{"issn":["0022-4715"],"eissn":["1572-9613"]},"volume":190,"article_type":"original","author":[{"full_name":"Sugimoto, Shoki","last_name":"Sugimoto","first_name":"Shoki"},{"orcid":"0000-0003-1106-327X","last_name":"Henheik","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha"},{"last_name":"Riabov","first_name":"Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","full_name":"Riabov, Volodymyr"},{"last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"}],"date_created":"2023-07-30T22:01:02Z","doi":"10.1007/s10955-023-03132-4","_id":"13317","scopus_import":"1","oa":1,"date_published":"2023-07-21T00:00:00Z","arxiv":1,"citation":{"apa":"Sugimoto, S., Henheik, S. J., Riabov, V., &#38; Erdös, L. (2023). Eigenstate thermalisation hypothesis for translation invariant spin systems. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-023-03132-4\">https://doi.org/10.1007/s10955-023-03132-4</a>","short":"S. Sugimoto, S.J. Henheik, V. Riabov, L. Erdös, Journal of Statistical Physics 190 (2023).","chicago":"Sugimoto, Shoki, Sven Joscha Henheik, Volodymyr Riabov, and László Erdös. “Eigenstate Thermalisation Hypothesis for Translation Invariant Spin Systems.” <i>Journal of Statistical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s10955-023-03132-4\">https://doi.org/10.1007/s10955-023-03132-4</a>.","mla":"Sugimoto, Shoki, et al. “Eigenstate Thermalisation Hypothesis for Translation Invariant Spin Systems.” <i>Journal of Statistical Physics</i>, vol. 190, no. 7, 128, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s10955-023-03132-4\">10.1007/s10955-023-03132-4</a>.","ama":"Sugimoto S, Henheik SJ, Riabov V, Erdös L. Eigenstate thermalisation hypothesis for translation invariant spin systems. <i>Journal of Statistical Physics</i>. 2023;190(7). doi:<a href=\"https://doi.org/10.1007/s10955-023-03132-4\">10.1007/s10955-023-03132-4</a>","ieee":"S. Sugimoto, S. J. Henheik, V. Riabov, and L. Erdös, “Eigenstate thermalisation hypothesis for translation invariant spin systems,” <i>Journal of Statistical Physics</i>, vol. 190, no. 7. Springer Nature, 2023.","ista":"Sugimoto S, Henheik SJ, Riabov V, Erdös L. 2023. Eigenstate thermalisation hypothesis for translation invariant spin systems. Journal of Statistical Physics. 190(7), 128."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"record":[{"status":"public","id":"20575","relation":"dissertation_contains"},{"relation":"dissertation_contains","id":"19540","status":"public"}]},"language":[{"iso":"eng"}],"ddc":["510","530"],"file":[{"content_type":"application/pdf","file_size":612755,"date_updated":"2023-07-31T07:49:31Z","success":1,"file_id":"13325","checksum":"c2ef6b2aecfee1ad6d03fab620507c2c","file_name":"2023_JourStatPhysics_Sugimoto.pdf","date_created":"2023-07-31T07:49:31Z","access_level":"open_access","creator":"dernst","relation":"main_file"}],"date_updated":"2026-04-07T12:37:10Z","external_id":{"isi":["001035677200002"],"arxiv":["2304.04213"]},"article_number":"128","status":"public","article_processing_charge":"Yes (in subscription journal)","publication":"Journal of Statistical Physics","department":[{"_id":"LaEr"}],"isi":1,"has_accepted_license":"1","ec_funded":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"year":"2023","publisher":"Springer Nature","month":"07","issue":"7","day":"21"},{"article_processing_charge":"Yes","publication":"Forum of Mathematics, Sigma","has_accepted_license":"1","isi":1,"department":[{"_id":"LaEr"},{"_id":"GradSch"}],"external_id":{"arxiv":["2301.05181"],"isi":["001051980200001"]},"article_number":"e74","status":"public","file":[{"success":1,"date_updated":"2023-09-20T11:09:35Z","file_size":852652,"content_type":"application/pdf","creator":"dernst","access_level":"open_access","date_created":"2023-09-20T11:09:35Z","file_name":"2023_ForumMathematics_Cipolloni.pdf","file_id":"14352","checksum":"eb747420e6a88a7796fa934151957676","relation":"main_file"}],"ddc":["510"],"date_updated":"2026-04-07T12:37:10Z","related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"}]},"language":[{"iso":"eng"}],"day":"23","publisher":"Cambridge University Press","corr_author":"1","month":"08","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"type":"journal_article","year":"2023","ec_funded":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"quality_controlled":"1","file_date_updated":"2023-09-20T11:09:35Z","publication_status":"published","title":"Gaussian fluctuations in the equipartition principle for Wigner matrices","oa_version":"Published Version","abstract":[{"lang":"eng","text":"The total energy of an eigenstate in a composite quantum system tends to be distributed equally among its constituents. We identify the quantum fluctuation around this equipartition principle in the simplest disordered quantum system consisting of linear combinations of Wigner matrices. As our main ingredient, we prove the Eigenstate Thermalisation Hypothesis and Gaussian fluctuation for general quadratic forms of the bulk eigenvectors of Wigner matrices with an arbitrary deformation."}],"oa":1,"date_published":"2023-08-23T00:00:00Z","citation":{"ieee":"G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Gaussian fluctuations in the equipartition principle for Wigner matrices,” <i>Forum of Mathematics, Sigma</i>, vol. 11. Cambridge University Press, 2023.","ista":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2023. Gaussian fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 11, e74.","apa":"Cipolloni, G., Erdös, L., Henheik, S. J., &#38; Kolupaiev, O. (2023). Gaussian fluctuations in the equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2023.70\">https://doi.org/10.1017/fms.2023.70</a>","short":"G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Forum of Mathematics, Sigma 11 (2023).","mla":"Cipolloni, Giorgio, et al. “Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>, vol. 11, e74, Cambridge University Press, 2023, doi:<a href=\"https://doi.org/10.1017/fms.2023.70\">10.1017/fms.2023.70</a>.","chicago":"Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2023. <a href=\"https://doi.org/10.1017/fms.2023.70\">https://doi.org/10.1017/fms.2023.70</a>.","ama":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Gaussian fluctuations in the equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2023;11. doi:<a href=\"https://doi.org/10.1017/fms.2023.70\">10.1017/fms.2023.70</a>"},"arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2023-09-17T22:01:09Z","author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603"},{"first_name":"Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"first_name":"Oleksii","orcid":"0000-0003-1491-4623","last_name":"Kolupaiev","full_name":"Kolupaiev, Oleksii","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61"}],"doi":"10.1017/fms.2023.70","_id":"14343","scopus_import":"1","volume":11,"publication_identifier":{"eissn":["2050-5094"]},"article_type":"original","intvolume":"        11","acknowledgement":"G.C. and L.E. gratefully acknowledge many discussions with Dominik Schröder at the preliminary stage of this project, especially his essential contribution to identify the correct generalisation of traceless observables to the deformed Wigner ensembles.\r\nL.E. and J.H. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331."},{"oa_version":"Preprint","title":"Prethermalization for deformed Wigner Matrices","publication_status":"draft","abstract":[{"lang":"eng","text":"We prove that a class of weakly perturbed Hamiltonians of the form $H_λ= H_0 + λW$, with $W$ being a Wigner matrix, exhibits prethermalization. That is, the time evolution generated by $H_λ$ relaxes to its ultimate thermal state via an intermediate prethermal state with a lifetime of order $λ^{-2}$. Moreover, we obtain a general relaxation formula, expressing the perturbed dynamics via the unperturbed dynamics and the ultimate thermal state. The proof relies on a two-resolvent law for the deformed Wigner matrix $H_λ$."}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2310.06677","open_access":"1"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","date_published":"2023-12-23T00:00:00Z","oa":1,"citation":{"ama":"Erdös L, Henheik SJ, Reker J, Riabov V. Prethermalization for deformed Wigner Matrices. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2310.06677\">10.48550/arXiv.2310.06677</a>","chicago":"Erdös, László, Sven Joscha Henheik, Jana Reker, and Volodymyr Riabov. “Prethermalization for Deformed Wigner Matrices.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2310.06677\">https://doi.org/10.48550/arXiv.2310.06677</a>.","mla":"Erdös, László, et al. “Prethermalization for Deformed Wigner Matrices.” <i>ArXiv</i>, 2310.06677, doi:<a href=\"https://doi.org/10.48550/arXiv.2310.06677\">10.48550/arXiv.2310.06677</a>.","short":"L. Erdös, S.J. Henheik, J. Reker, V. Riabov, ArXiv (n.d.).","apa":"Erdös, L., Henheik, S. J., Reker, J., &#38; Riabov, V. (n.d.). Prethermalization for deformed Wigner Matrices. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2310.06677\">https://doi.org/10.48550/arXiv.2310.06677</a>","ista":"Erdös L, Henheik SJ, Reker J, Riabov V. Prethermalization for deformed Wigner Matrices. arXiv, 2310.06677.","ieee":"L. Erdös, S. J. Henheik, J. Reker, and V. Riabov, “Prethermalization for deformed Wigner Matrices,” <i>arXiv</i>. ."},"arxiv":1,"_id":"17174","OA_place":"repository","date_created":"2024-06-26T08:56:52Z","author":[{"last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X"},{"full_name":"Reker, Jana","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","first_name":"Jana","last_name":"Reker"},{"full_name":"Riabov, Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","first_name":"Volodymyr","last_name":"Riabov"}],"doi":"10.48550/arXiv.2310.06677","date_updated":"2026-04-07T13:02:12Z","related_material":{"record":[{"id":"18764","status":"public","relation":"later_version"},{"relation":"dissertation_contains","id":"20575","status":"public"},{"id":"17164","status":"public","relation":"dissertation_contains"}]},"language":[{"iso":"eng"}],"publication":"arXiv","department":[{"_id":"LaEr"}],"article_processing_charge":"No","status":"public","external_id":{"arxiv":["2310.06677"]},"article_number":"2310.06677","year":"2023","project":[{"call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"type":"preprint","ec_funded":1,"day":"23","corr_author":"1","month":"12"},{"article_processing_charge":"No","publication":"arXiv","department":[{"_id":"LaEr"}],"external_id":{"arxiv":["2307.11028"]},"article_number":"2307.11028","status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2307.11028"}],"publication_status":"draft","date_updated":"2026-04-07T13:02:12Z","title":"Multi-point functional central limit theorem for Wigner Matrices","oa_version":"Preprint","related_material":{"record":[{"status":"public","id":"18762","relation":"later_version"},{"id":"17164","status":"public","relation":"dissertation_contains"}]},"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"Consider the random variable $\\mathrm{Tr}( f_1(W)A_1\\dots f_k(W)A_k)$ where $W$ is an $N\\times N$ Hermitian Wigner matrix, $k\\in\\mathbb{N}$, and choose (possibly $N$-dependent) regular functions $f_1,\\dots, f_k$ as well as bounded deterministic matrices $A_1,\\dots,A_k$. We give a functional central limit theorem showing that the fluctuations around the expectation are Gaussian. Moreover, we determine the limiting covariance structure and give explicit error bounds in terms of the scaling of $f_1,\\dots,f_k$ and the number of traceless matrices among $A_1,\\dots,A_k$, thus extending the results of [Cipolloni, Erdős, Schröder 2023] to products of arbitrary length $k\\geq2$. As an application, we consider the fluctuation of $\\mathrm{Tr}(\\mathrm{e}^{\\mathrm{i} tW}A_1\\mathrm{e}^{-\\mathrm{i} tW}A_2)$ around its thermal value $\\mathrm{Tr}(A_1)\\mathrm{Tr}(A_2)$ when $t$ is large and give an explicit formula for the variance."}],"oa":1,"date_published":"2023-07-21T00:00:00Z","arxiv":1,"citation":{"apa":"Reker, J. (n.d.). Multi-point functional central limit theorem for Wigner Matrices. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2307.11028\">https://doi.org/10.48550/arXiv.2307.11028</a>","chicago":"Reker, Jana. “Multi-Point Functional Central Limit Theorem for Wigner Matrices.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2307.11028\">https://doi.org/10.48550/arXiv.2307.11028</a>.","short":"J. Reker, ArXiv (n.d.).","mla":"Reker, Jana. “Multi-Point Functional Central Limit Theorem for Wigner Matrices.” <i>ArXiv</i>, 2307.11028, doi:<a href=\"https://doi.org/10.48550/arXiv.2307.11028\">10.48550/arXiv.2307.11028</a>.","ama":"Reker J. Multi-point functional central limit theorem for Wigner Matrices. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2307.11028\">10.48550/arXiv.2307.11028</a>","ieee":"J. Reker, “Multi-point functional central limit theorem for Wigner Matrices,” <i>arXiv</i>. .","ista":"Reker J. Multi-point functional central limit theorem for Wigner Matrices. arXiv, 2307.11028."},"day":"21","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Jana","last_name":"Reker","full_name":"Reker, Jana","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9"}],"date_created":"2024-06-26T08:54:56Z","doi":"10.48550/arXiv.2307.11028","_id":"17173","OA_place":"repository","month":"07","type":"preprint","year":"2023"},{"citation":{"ista":"Henheik SJ, Tumulka R. 2022. Interior-boundary conditions for the Dirac equation at point sources in three dimensions. Journal of Mathematical Physics. 63(12), 122302.","ieee":"S. J. Henheik and R. Tumulka, “Interior-boundary conditions for the Dirac equation at point sources in three dimensions,” <i>Journal of Mathematical Physics</i>, vol. 63, no. 12. AIP Publishing, 2022.","ama":"Henheik SJ, Tumulka R. Interior-boundary conditions for the Dirac equation at point sources in three dimensions. <i>Journal of Mathematical Physics</i>. 2022;63(12). doi:<a href=\"https://doi.org/10.1063/5.0104675\">10.1063/5.0104675</a>","chicago":"Henheik, Sven Joscha, and Roderich Tumulka. “Interior-Boundary Conditions for the Dirac Equation at Point Sources in Three Dimensions.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2022. <a href=\"https://doi.org/10.1063/5.0104675\">https://doi.org/10.1063/5.0104675</a>.","short":"S.J. Henheik, R. Tumulka, Journal of Mathematical Physics 63 (2022).","mla":"Henheik, Sven Joscha, and Roderich Tumulka. “Interior-Boundary Conditions for the Dirac Equation at Point Sources in Three Dimensions.” <i>Journal of Mathematical Physics</i>, vol. 63, no. 12, 122302, AIP Publishing, 2022, doi:<a href=\"https://doi.org/10.1063/5.0104675\">10.1063/5.0104675</a>.","apa":"Henheik, S. J., &#38; Tumulka, R. (2022). Interior-boundary conditions for the Dirac equation at point sources in three dimensions. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0104675\">https://doi.org/10.1063/5.0104675</a>"},"oa":1,"date_published":"2022-12-01T00:00:00Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"last_name":"Henheik","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha"},{"last_name":"Tumulka","first_name":"Roderich","full_name":"Tumulka, Roderich"}],"doi":"10.1063/5.0104675","date_created":"2023-01-08T23:00:53Z","scopus_import":"1","_id":"12110","article_type":"original","publication_identifier":{"issn":["0022-2488"]},"volume":63,"acknowledgement":"J.H. gratefully acknowledges the partial financial support by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331.\r\n","intvolume":"        63","quality_controlled":"1","file_date_updated":"2023-01-20T11:58:59Z","publication_status":"published","oa_version":"Published Version","title":"Interior-boundary conditions for the Dirac equation at point sources in three dimensions","abstract":[{"text":"A recently proposed approach for avoiding the ultraviolet divergence of Hamiltonians with particle creation is based on interior-boundary conditions (IBCs). The approach works well in the non-relativistic case, i.e., for the Laplacian operator. Here, we study how the approach can be applied to Dirac operators. While this has successfully been done already in one space dimension, and more generally for codimension-1 boundaries, the situation of point sources in three dimensions corresponds to a codimension-3 boundary. One would expect that, for such a boundary, Dirac operators do not allow for boundary conditions because they are known not to allow for point interactions in 3D, which also correspond to a boundary condition. Indeed, we confirm this expectation here by proving that there is no self-adjoint operator on a (truncated) Fock space that would correspond to a Dirac operator with an IBC at configurations with a particle at the origin. However, we also present a positive result showing that there are self-adjoint operators with an IBC (on the boundary consisting of configurations with a particle at the origin) that are away from those configurations, given by a Dirac operator plus a sufficiently strong Coulomb potential.","lang":"eng"}],"day":"01","issue":"12","publisher":"AIP Publishing","month":"12","corr_author":"1","type":"journal_article","project":[{"grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"year":"2022","ec_funded":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"article_processing_charge":"No","department":[{"_id":"LaEr"}],"has_accepted_license":"1","isi":1,"publication":"Journal of Mathematical Physics","article_number":"122302","external_id":{"isi":["000900748900002"]},"status":"public","file":[{"relation":"main_file","creator":"dernst","access_level":"open_access","file_id":"12327","date_created":"2023-01-20T11:58:59Z","checksum":"5150287295e0ce4f12462c990744d65d","file_name":"2022_JourMathPhysics_Henheik.pdf","success":1,"date_updated":"2023-01-20T11:58:59Z","file_size":5436804,"content_type":"application/pdf"}],"date_updated":"2025-04-14T07:57:18Z","ddc":["510"],"language":[{"iso":"eng"}]},{"ec_funded":1,"keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331"}],"year":"2022","publisher":"Cambridge University Press","corr_author":"1","month":"10","day":"27","language":[{"iso":"eng"}],"ddc":["510"],"file":[{"content_type":"application/pdf","date_updated":"2023-01-24T10:02:40Z","file_size":817089,"success":1,"relation":"main_file","checksum":"94a049aeb1eea5497aa097712a73c400","file_name":"2022_ForumMath_Cipolloni.pdf","file_id":"12356","date_created":"2023-01-24T10:02:40Z","creator":"dernst","access_level":"open_access"}],"date_updated":"2025-04-14T07:57:18Z","external_id":{"isi":["000873719200001"]},"article_number":"e96","status":"public","article_processing_charge":"No","publication":"Forum of Mathematics, Sigma","has_accepted_license":"1","isi":1,"department":[{"_id":"LaEr"}],"intvolume":"        10","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.","volume":10,"publication_identifier":{"issn":["2050-5094"]},"article_type":"original","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","first_name":"Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László"},{"last_name":"Schröder","orcid":"0000-0002-2904-1856","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"date_created":"2023-01-12T12:07:30Z","doi":"10.1017/fms.2022.86","_id":"12148","scopus_import":"1","oa":1,"date_published":"2022-10-27T00:00:00Z","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 10, e96.","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.","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>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022).","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>.","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>.","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>"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","abstract":[{"lang":"eng","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."}],"publication_status":"published","oa_version":"Published Version","title":"Rank-uniform local law for Wigner matrices","file_date_updated":"2023-01-24T10:02:40Z","quality_controlled":"1"},{"type":"journal_article","year":"2022","keyword":["Analysis"],"issue":"3","day":"01","publisher":"Society for Industrial and Applied Mathematics","corr_author":"1","month":"07","date_updated":"2025-09-10T09:51:27Z","language":[{"iso":"eng"}],"article_processing_charge":"No","publication":"SIAM Journal on Matrix Analysis and Applications","isi":1,"department":[{"_id":"LaEr"}],"external_id":{"arxiv":["2105.13719"],"isi":["001125796400002"]},"status":"public","publication_identifier":{"eissn":["1095-7162"],"issn":["0895-4798"]},"volume":43,"article_type":"original","intvolume":"        43","date_published":"2022-07-01T00:00:00Z","oa":1,"arxiv":1,"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>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, SIAM Journal on Matrix Analysis and Applications 43 (2022) 1469–1487.","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>.","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>.","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>","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.","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."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"date_created":"2023-01-12T12:12:38Z","doi":"10.1137/21m1424408","_id":"12179","scopus_import":"1","publication_status":"published","title":"On the condition number of the shifted real Ginibre ensemble","oa_version":"Preprint","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]."}],"quality_controlled":"1","page":"1469-1487","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2105.13719","open_access":"1"}]},{"language":[{"iso":"eng"}],"date_updated":"2025-04-14T07:50:40Z","external_id":{"isi":["000854878500001"],"arxiv":["2102.02037"]},"status":"public","article_processing_charge":"No","department":[{"_id":"LaEr"}],"isi":1,"publication":"Journal of the London Mathematical Society","ec_funded":1,"keyword":["General Mathematics"],"type":"journal_article","project":[{"_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Geometric study of Wasserstein spaces and free probability","grant_number":"846294"}],"year":"2022","publisher":"Wiley","month":"09","issue":"4","day":"18","abstract":[{"lang":"eng","text":"Motivated by Kloeckner’s result on the isometry group of the quadratic Wasserstein space W2(Rn), we describe the isometry group Isom(Wp(E)) for all parameters 0 < p < ∞ and for all separable real Hilbert spaces E. In particular, we show that Wp(X) is isometrically rigid for all Polish space X whenever 0 < p < 1. This is a consequence of our more general result: we prove that W1(X) is isometrically rigid if X is a complete separable metric space that satisfies the strict triangle inequality. Furthermore, we show that this latter rigidity result does not generalise to parameters p > 1, by solving Kloeckner’s problem affirmatively on the existence of mass-splitting isometries. "}],"publication_status":"published","title":"The isometry group of Wasserstein spaces: The Hilbertian case","oa_version":"Preprint","page":"3865-3894","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2102.02037"}],"quality_controlled":"1","acknowledgement":"Geher was supported by the Leverhulme Trust Early Career Fellowship (ECF-2018-125), and also by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. K115383 and K134944).\r\nTitkos was supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. PD128374, grant no. K115383 and K134944), by the J´anos Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the UNKP-20-5-BGE-1 New National Excellence Program of the ´Ministry of Innovation and Technology.\r\nVirosztek was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 846294, by the Momentum program of the Hungarian Academy of Sciences under grant agreement no. LP2021-15/2021, and partially supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grants no. K124152 and no. KH129601). ","intvolume":"       106","article_type":"original","volume":106,"publication_identifier":{"issn":["0024-6107"],"eissn":["1469-7750"]},"doi":"10.1112/jlms.12676","author":[{"last_name":"Gehér","first_name":"György Pál","full_name":"Gehér, György Pál"},{"full_name":"Titkos, Tamás","last_name":"Titkos","first_name":"Tamás"},{"full_name":"Virosztek, Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel","last_name":"Virosztek","orcid":"0000-0003-1109-5511"}],"date_created":"2023-01-16T09:46:13Z","scopus_import":"1","_id":"12214","arxiv":1,"citation":{"ista":"Gehér GP, Titkos T, Virosztek D. 2022. The isometry group of Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical Society. 106(4), 3865–3894.","ieee":"G. P. Gehér, T. Titkos, and D. Virosztek, “The isometry group of Wasserstein spaces: The Hilbertian case,” <i>Journal of the London Mathematical Society</i>, vol. 106, no. 4. Wiley, pp. 3865–3894, 2022.","short":"G.P. Gehér, T. Titkos, D. Virosztek, Journal of the London Mathematical Society 106 (2022) 3865–3894.","mla":"Gehér, György Pál, et al. “The Isometry Group of Wasserstein Spaces: The Hilbertian Case.” <i>Journal of the London Mathematical Society</i>, vol. 106, no. 4, Wiley, 2022, pp. 3865–94, doi:<a href=\"https://doi.org/10.1112/jlms.12676\">10.1112/jlms.12676</a>.","chicago":"Gehér, György Pál, Tamás Titkos, and Daniel Virosztek. “The Isometry Group of Wasserstein Spaces: The Hilbertian Case.” <i>Journal of the London Mathematical Society</i>. Wiley, 2022. <a href=\"https://doi.org/10.1112/jlms.12676\">https://doi.org/10.1112/jlms.12676</a>.","ama":"Gehér GP, Titkos T, Virosztek D. The isometry group of Wasserstein spaces: The Hilbertian case. <i>Journal of the London Mathematical Society</i>. 2022;106(4):3865-3894. doi:<a href=\"https://doi.org/10.1112/jlms.12676\">10.1112/jlms.12676</a>","apa":"Gehér, G. P., Titkos, T., &#38; Virosztek, D. (2022). The isometry group of Wasserstein spaces: The Hilbertian case. <i>Journal of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/jlms.12676\">https://doi.org/10.1112/jlms.12676</a>"},"date_published":"2022-09-18T00:00:00Z","oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"date_created":"2023-01-16T09:50:26Z","author":[{"first_name":"Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","first_name":"Dominik J"}],"doi":"10.1007/s00023-022-01188-8","scopus_import":"1","_id":"12232","citation":{"mla":"Cipolloni, Giorgio, et al. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” <i>Annales Henri Poincaré</i>, vol. 23, no. 11, Springer Nature, 2022, pp. 3981–4002, doi:<a href=\"https://doi.org/10.1007/s00023-022-01188-8\">10.1007/s00023-022-01188-8</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” <i>Annales Henri Poincaré</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00023-022-01188-8\">https://doi.org/10.1007/s00023-022-01188-8</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Density of small singular values of the shifted real Ginibre ensemble. <i>Annales Henri Poincaré</i>. 2022;23(11):3981-4002. doi:<a href=\"https://doi.org/10.1007/s00023-022-01188-8\">10.1007/s00023-022-01188-8</a>","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Density of small singular values of the shifted real Ginibre ensemble. <i>Annales Henri Poincaré</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-022-01188-8\">https://doi.org/10.1007/s00023-022-01188-8</a>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. 23(11), 3981–4002.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Density of small singular values of the shifted real Ginibre ensemble,” <i>Annales Henri Poincaré</i>, vol. 23, no. 11. Springer Nature, pp. 3981–4002, 2022."},"date_published":"2022-11-01T00:00:00Z","oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"Open access funding provided by Swiss Federal Institute of Technology Zurich. Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","intvolume":"        23","article_type":"original","publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]},"volume":23,"page":"3981-4002","quality_controlled":"1","file_date_updated":"2023-01-27T11:06:47Z","abstract":[{"text":"We derive a precise asymptotic formula for the density of the small singular values of the real Ginibre matrix ensemble shifted by a complex parameter z as the dimension tends to infinity. For z away from the real axis the formula coincides with that for the complex Ginibre ensemble we derived earlier in Cipolloni et al. (Prob Math Phys 1:101–146, 2020). On the level of the one-point function of the low lying singular values we thus confirm the transition from real to complex Ginibre ensembles as the shift parameter z becomes genuinely complex; the analogous phenomenon has been well known for eigenvalues. We use the superbosonization formula (Littelmann et al. in Comm Math Phys 283:343–395, 2008) in a regime where the main contribution comes from a three dimensional saddle manifold.","lang":"eng"}],"publication_status":"published","oa_version":"Published Version","title":"Density of small singular values of the shifted real Ginibre ensemble","publisher":"Springer Nature","month":"11","day":"01","issue":"11","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"type":"journal_article","year":"2022","external_id":{"isi":["000796323500001"]},"status":"public","article_processing_charge":"No","isi":1,"has_accepted_license":"1","department":[{"_id":"LaEr"}],"publication":"Annales Henri Poincaré","language":[{"iso":"eng"}],"file":[{"file_id":"12424","file_name":"2022_AnnalesHenriP_Cipolloni.pdf","checksum":"5582f059feeb2f63e2eb68197a34d7dc","date_created":"2023-01-27T11:06:47Z","access_level":"open_access","creator":"dernst","relation":"main_file","date_updated":"2023-01-27T11:06:47Z","file_size":1333638,"content_type":"application/pdf","success":1}],"ddc":["510"],"date_updated":"2023-08-04T09:33:52Z"},{"file_date_updated":"2023-01-30T08:01:10Z","quality_controlled":"1","publication_status":"published","oa_version":"Published Version","title":"Directional extremal statistics for Ginibre eigenvalues","abstract":[{"lang":"eng","text":"We consider the eigenvalues of a large dimensional real or complex Ginibre matrix in the region of the complex plane where their real parts reach their maximum value. This maximum follows the Gumbel distribution and that these extreme eigenvalues form a Poisson point process as the dimension asymptotically tends to infinity. In the complex case, these facts have already been established by Bender [Probab. Theory Relat. Fields 147, 241 (2010)] and in the real case by Akemann and Phillips [J. Stat. Phys. 155, 421 (2014)] even for the more general elliptic ensemble with a sophisticated saddle point analysis. The purpose of this article is to give a very short direct proof in the Ginibre case with an effective error term. Moreover, our estimates on the correlation kernel in this regime serve as a key input for accurately locating [Formula: see text] for any large matrix X with i.i.d. entries in the companion paper [G. Cipolloni et al., arXiv:2206.04448 (2022)]. "}],"date_published":"2022-10-14T00:00:00Z","oa":1,"citation":{"apa":"Cipolloni, G., Erdös, L., Schröder, D. J., &#38; Xu, Y. (2022). Directional extremal statistics for Ginibre eigenvalues. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0104290\">https://doi.org/10.1063/5.0104290</a>","ama":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. Directional extremal statistics for Ginibre eigenvalues. <i>Journal of Mathematical Physics</i>. 2022;63(10). doi:<a href=\"https://doi.org/10.1063/5.0104290\">10.1063/5.0104290</a>","mla":"Cipolloni, Giorgio, et al. “Directional Extremal Statistics for Ginibre Eigenvalues.” <i>Journal of Mathematical Physics</i>, vol. 63, no. 10, 103303, AIP Publishing, 2022, doi:<a href=\"https://doi.org/10.1063/5.0104290\">10.1063/5.0104290</a>.","chicago":"Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “Directional Extremal Statistics for Ginibre Eigenvalues.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2022. <a href=\"https://doi.org/10.1063/5.0104290\">https://doi.org/10.1063/5.0104290</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, Journal of Mathematical Physics 63 (2022).","ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “Directional extremal statistics for Ginibre eigenvalues,” <i>Journal of Mathematical Physics</i>, vol. 63, no. 10. AIP Publishing, 2022.","ista":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2022. Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. 63(10), 103303."},"arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603"},{"first_name":"Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"},{"id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","full_name":"Xu, Yuanyuan","last_name":"Xu","orcid":"0000-0003-1559-1205","first_name":"Yuanyuan"}],"date_created":"2023-01-16T09:52:58Z","doi":"10.1063/5.0104290","_id":"12243","scopus_import":"1","publication_identifier":{"issn":["0022-2488"],"eissn":["1089-7658"]},"volume":63,"article_type":"original","intvolume":"        63","acknowledgement":"The authors are grateful to G. Akemann for bringing Refs. 19 and 24–26 to their attention. Discussions with Guillaume Dubach on a preliminary version of this project are acknowledged.\r\nL.E. and Y.X. were supported by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331. D.S. was supported by Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation.","article_processing_charge":"Yes (via OA deal)","publication":"Journal of Mathematical Physics","has_accepted_license":"1","isi":1,"department":[{"_id":"LaEr"}],"external_id":{"arxiv":["2206.04443"],"isi":["000869715800001"]},"article_number":"103303","status":"public","ddc":["510","530"],"file":[{"checksum":"2db278ae5b07f345a7e3fec1f92b5c33","file_id":"12436","file_name":"2022_JourMathPhysics_Cipolloni2.pdf","date_created":"2023-01-30T08:01:10Z","access_level":"open_access","creator":"dernst","relation":"main_file","content_type":"application/pdf","file_size":7356807,"date_updated":"2023-01-30T08:01:10Z","success":1}],"date_updated":"2025-04-14T07:57:18Z","language":[{"iso":"eng"}],"issue":"10","day":"14","publisher":"AIP Publishing","month":"10","type":"journal_article","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"year":"2022","ec_funded":1,"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"}},{"year":"2022","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"type":"journal_article","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"ec_funded":1,"day":"12","month":"09","corr_author":"1","publisher":"Institute of Mathematical Statistics","date_updated":"2025-04-14T07:57:19Z","ddc":["510"],"file":[{"success":1,"content_type":"application/pdf","date_updated":"2023-01-30T11:59:21Z","file_size":502149,"creator":"dernst","access_level":"open_access","file_name":"2022_ElecJournProbability_Cipolloni.pdf","date_created":"2023-01-30T11:59:21Z","checksum":"bb647b48fbdb59361210e425c220cdcb","file_id":"12464","relation":"main_file"}],"language":[{"iso":"eng"}],"has_accepted_license":"1","isi":1,"department":[{"_id":"LaEr"}],"publication":"Electronic Journal of Probability","article_processing_charge":"No","status":"public","external_id":{"isi":["000910863700003"]},"article_type":"original","volume":27,"publication_identifier":{"eissn":["1083-6489"]},"acknowledgement":"L. Erdős was supported by ERC Advanced Grant “RMTBeyond” No. 101020331. D. Schröder was supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","intvolume":"        27","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 27, 1–38.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal multi-resolvent local laws for Wigner matrices,” <i>Electronic Journal of Probability</i>, vol. 27. Institute of Mathematical Statistics, pp. 1–38, 2022.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 27 (2022) 1–38.","mla":"Cipolloni, Giorgio, et al. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” <i>Electronic Journal of Probability</i>, vol. 27, Institute of Mathematical Statistics, 2022, pp. 1–38, doi:<a href=\"https://doi.org/10.1214/22-ejp838\">10.1214/22-ejp838</a>.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics, 2022. <a href=\"https://doi.org/10.1214/22-ejp838\">https://doi.org/10.1214/22-ejp838</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Optimal multi-resolvent local laws for Wigner matrices. <i>Electronic Journal of Probability</i>. 2022;27:1-38. doi:<a href=\"https://doi.org/10.1214/22-ejp838\">10.1214/22-ejp838</a>","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Optimal multi-resolvent local laws for Wigner matrices. <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-ejp838\">https://doi.org/10.1214/22-ejp838</a>"},"oa":1,"date_published":"2022-09-12T00:00:00Z","scopus_import":"1","_id":"12290","date_created":"2023-01-16T10:04:38Z","author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni"},{"orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder"}],"doi":"10.1214/22-ejp838","title":"Optimal multi-resolvent local laws for Wigner matrices","oa_version":"Published Version","publication_status":"published","abstract":[{"lang":"eng","text":"We prove local laws, i.e. optimal concentration estimates for arbitrary products of resolvents of a Wigner random matrix with deterministic matrices in between. We find that the size of such products heavily depends on whether some of the deterministic matrices are traceless. Our estimates correctly account for this dependence and they hold optimally down to the smallest possible spectral scale."}],"file_date_updated":"2023-01-30T11:59:21Z","quality_controlled":"1","page":"1-38"},{"type":"journal_article","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"year":"2022","ec_funded":1,"keyword":["mathematical physics","statistical and nonlinear physics"],"day":"03","issue":"1","publisher":"AIP Publishing","month":"01","date_updated":"2025-04-14T07:57:17Z","language":[{"iso":"eng"}],"article_processing_charge":"No","publication":"Journal of Mathematical Physics","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"isi":1,"external_id":{"arxiv":["2012.15238"],"isi":["000739446000009"]},"article_number":"011901","status":"public","publication_identifier":{"eissn":["1089-7658"],"issn":["0022-2488"]},"volume":63,"article_type":"original","intvolume":"        63","acknowledgement":"J.H. acknowledges partial financial support from ERC Advanced Grant “RMTBeyond” No. 101020331.","date_published":"2022-01-03T00:00:00Z","oa":1,"citation":{"apa":"Henheik, S. J., &#38; Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0051632\">https://doi.org/10.1063/5.0051632</a>","ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. <i>Journal of Mathematical Physics</i>. 2022;63(1). doi:<a href=\"https://doi.org/10.1063/5.0051632\">10.1063/5.0051632</a>","short":"S.J. Henheik, S. Teufel, Journal of Mathematical Physics 63 (2022).","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Uniform Gap.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2022. <a href=\"https://doi.org/10.1063/5.0051632\">https://doi.org/10.1063/5.0051632</a>.","mla":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Uniform Gap.” <i>Journal of Mathematical Physics</i>, vol. 63, no. 1, 011901, AIP Publishing, 2022, doi:<a href=\"https://doi.org/10.1063/5.0051632\">10.1063/5.0051632</a>.","ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap,” <i>Journal of Mathematical Physics</i>, vol. 63, no. 1. AIP Publishing, 2022.","ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. 63(1), 011901."},"arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha"},{"full_name":"Teufel, Stefan","last_name":"Teufel","first_name":"Stefan"}],"doi":"10.1063/5.0051632","date_created":"2022-01-03T12:19:48Z","_id":"10600","scopus_import":"1","publication_status":"published","title":"Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap","oa_version":"Preprint","abstract":[{"text":"We show that recent results on adiabatic theory for interacting gapped many-body systems on finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalized super-adiabatic theorem for the automorphism group describing the infinite volume dynamics on the quasi-local algebra of observables. The key assumption is the existence of a sequence of gapped finite volume Hamiltonians, which generates the same infinite volume dynamics in the thermodynamic limit. Our adiabatic theorem also holds for certain perturbations of gapped ground states that close the spectral gap (so it is also an adiabatic theorem for resonances and, in this sense, “generalized”), and it provides an adiabatic approximation to all orders in the adiabatic parameter (a property often called “super-adiabatic”). In addition to the existing results for finite lattices, we also perform a resummation of the adiabatic expansion and allow for observables that are not strictly local. Finally, as an application, we prove the validity of linear and higher order response theory for our class of perturbations for infinite systems. While we consider the result and its proof as new and interesting in itself, we also lay the foundation for the proof of an adiabatic theorem for systems with a gap only in the bulk, which will be presented in a follow-up article.","lang":"eng"}],"quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2012.15238","open_access":"1"}]},{"file_date_updated":"2022-01-19T09:27:43Z","quality_controlled":"1","publication_status":"published","title":"Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk","oa_version":"Published Version","abstract":[{"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","lang":"eng"}],"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>","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>.","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>.","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>","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."},"arxiv":1,"oa":1,"date_published":"2022-01-18T00:00:00Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_created":"2022-01-18T16:18:51Z","doi":"10.1017/fms.2021.80","author":[{"last_name":"Henheik","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha"},{"first_name":"Stefan","last_name":"Teufel","full_name":"Teufel, Stefan"}],"scopus_import":"1","_id":"10643","article_type":"original","publication_identifier":{"eissn":["2050-5094"]},"volume":10,"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.","intvolume":"        10","article_processing_charge":"Yes","isi":1,"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"has_accepted_license":"1","publication":"Forum of Mathematics, Sigma","article_number":"e4","external_id":{"arxiv":["2012.15239"],"isi":["000743615000001"]},"status":"public","ddc":["510"],"file":[{"relation":"main_file","access_level":"open_access","creator":"cchlebak","date_created":"2022-01-19T09:27:43Z","file_id":"10646","file_name":"2022_ForumMathSigma_Henheik.pdf","checksum":"87592a755adcef22ea590a99dc728dd3","success":1,"date_updated":"2022-01-19T09:27:43Z","file_size":705323,"content_type":"application/pdf"}],"date_updated":"2025-04-14T07:57:17Z","language":[{"iso":"eng"}],"day":"18","publisher":"Cambridge University Press","month":"01","corr_author":"1","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"type":"journal_article","year":"2022","ec_funded":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"keyword":["computational mathematics","discrete mathematics and combinatorics","geometry and topology","mathematical physics","statistics and probability","algebra and number theory","theoretical computer science","analysis"]}]