[{"page":"1270-1334","title":"Local single ring theorem on optimal scale","external_id":{"arxiv":["1612.05920"],"isi":["000466616100003"]},"volume":47,"year":"2019","project":[{"name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7"}],"publication":"Annals of Probability","date_created":"2019-06-02T21:59:13Z","article_processing_charge":"No","publication_identifier":{"issn":["0091-1798"]},"department":[{"_id":"LaEr"}],"quality_controlled":"1","scopus_import":"1","citation":{"ama":"Bao Z, Erdös L, Schnelli K. Local single ring theorem on optimal scale. <i>Annals of Probability</i>. 2019;47(3):1270-1334. doi:<a href=\"https://doi.org/10.1214/18-AOP1284\">10.1214/18-AOP1284</a>","ista":"Bao Z, Erdös L, Schnelli K. 2019. Local single ring theorem on optimal scale. Annals of Probability. 47(3), 1270–1334.","mla":"Bao, Zhigang, et al. “Local Single Ring Theorem on Optimal Scale.” <i>Annals of Probability</i>, vol. 47, no. 3, Institute of Mathematical Statistics, 2019, pp. 1270–334, doi:<a href=\"https://doi.org/10.1214/18-AOP1284\">10.1214/18-AOP1284</a>.","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Local single ring theorem on optimal scale,” <i>Annals of Probability</i>, vol. 47, no. 3. Institute of Mathematical Statistics, pp. 1270–1334, 2019.","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Single Ring Theorem on Optimal Scale.” <i>Annals of Probability</i>. Institute of Mathematical Statistics, 2019. <a href=\"https://doi.org/10.1214/18-AOP1284\">https://doi.org/10.1214/18-AOP1284</a>.","short":"Z. Bao, L. Erdös, K. Schnelli, Annals of Probability 47 (2019) 1270–1334.","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2019). Local single ring theorem on optimal scale. <i>Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/18-AOP1284\">https://doi.org/10.1214/18-AOP1284</a>"},"author":[{"orcid":"0000-0003-3036-1475","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","last_name":"Bao","first_name":"Zhigang","full_name":"Bao, Zhigang"},{"full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László"},{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","last_name":"Schnelli","orcid":"0000-0003-0954-3231","first_name":"Kevin","full_name":"Schnelli, Kevin"}],"_id":"6511","intvolume":"        47","publisher":"Institute of Mathematical Statistics","type":"journal_article","isi":1,"publication_status":"published","abstract":[{"text":"Let U and V be two independent N by N random matrices that are distributed according to Haar measure on U(N). Let Σ be a nonnegative deterministic N by N matrix. The single ring theorem [Ann. of Math. (2) 174 (2011) 1189–1217] asserts that the empirical eigenvalue distribution of the matrix X:=UΣV∗ converges weakly, in the limit of large N, to a deterministic measure which is supported on a single ring centered at the origin in ℂ. Within the bulk regime, that is, in the interior of the single ring, we establish the convergence of the empirical eigenvalue distribution on the optimal local scale of order N−1/2+ε and establish the optimal convergence rate. The same results hold true when U and V are Haar distributed on O(N).","lang":"eng"}],"date_published":"2019-05-01T00:00:00Z","status":"public","month":"05","main_file_link":[{"url":"https://arxiv.org/abs/1612.05920","open_access":"1"}],"doi":"10.1214/18-AOP1284","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"3","date_updated":"2025-07-10T11:53:28Z","oa_version":"Preprint","arxiv":1,"oa":1,"language":[{"iso":"eng"}],"ec_funded":1,"day":"01"},{"isi":1,"type":"journal_article","publisher":"Elsevier","intvolume":"       480","_id":"6843","author":[{"full_name":"Gehér, György Pál","last_name":"Gehér","first_name":"György Pál"},{"full_name":"Titkos, Tamás","last_name":"Titkos","first_name":"Tamás"},{"full_name":"Virosztek, Daniel","first_name":"Daniel","orcid":"0000-0003-1109-5511","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","last_name":"Virosztek"}],"citation":{"chicago":"Gehér, György Pál, Tamás Titkos, and Daniel Virosztek. “On Isometric Embeddings of Wasserstein Spaces – the Discrete Case.” <i>Journal of Mathematical Analysis and Applications</i>. Elsevier, 2019. <a href=\"https://doi.org/10.1016/j.jmaa.2019.123435\">https://doi.org/10.1016/j.jmaa.2019.123435</a>.","apa":"Gehér, G. P., Titkos, T., &#38; Virosztek, D. (2019). On isometric embeddings of Wasserstein spaces – the discrete case. <i>Journal of Mathematical Analysis and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jmaa.2019.123435\">https://doi.org/10.1016/j.jmaa.2019.123435</a>","short":"G.P. Gehér, T. Titkos, D. Virosztek, Journal of Mathematical Analysis and Applications 480 (2019).","ama":"Gehér GP, Titkos T, Virosztek D. On isometric embeddings of Wasserstein spaces – the discrete case. <i>Journal of Mathematical Analysis and Applications</i>. 2019;480(2). doi:<a href=\"https://doi.org/10.1016/j.jmaa.2019.123435\">10.1016/j.jmaa.2019.123435</a>","ieee":"G. P. Gehér, T. Titkos, and D. Virosztek, “On isometric embeddings of Wasserstein spaces – the discrete case,” <i>Journal of Mathematical Analysis and Applications</i>, vol. 480, no. 2. Elsevier, 2019.","mla":"Gehér, György Pál, et al. “On Isometric Embeddings of Wasserstein Spaces – the Discrete Case.” <i>Journal of Mathematical Analysis and Applications</i>, vol. 480, no. 2, 123435, Elsevier, 2019, doi:<a href=\"https://doi.org/10.1016/j.jmaa.2019.123435\">10.1016/j.jmaa.2019.123435</a>.","ista":"Gehér GP, Titkos T, Virosztek D. 2019. On isometric embeddings of Wasserstein spaces – the discrete case. Journal of Mathematical Analysis and Applications. 480(2), 123435."},"scopus_import":"1","quality_controlled":"1","article_number":"123435","department":[{"_id":"LaEr"}],"publication_identifier":{"eissn":["1096-0813"],"issn":["0022-247X"]},"article_processing_charge":"No","date_created":"2019-09-01T22:01:01Z","publication":"Journal of Mathematical Analysis and Applications","project":[{"name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"291734"}],"year":"2019","volume":480,"external_id":{"isi":["000486563900031"],"arxiv":["1809.01101"]},"title":"On isometric embeddings of Wasserstein spaces – the discrete case","article_type":"original","day":"15","ec_funded":1,"oa":1,"language":[{"iso":"eng"}],"arxiv":1,"oa_version":"Preprint","date_updated":"2025-07-10T11:53:55Z","issue":"2","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1016/j.jmaa.2019.123435","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1809.01101"}],"month":"12","status":"public","date_published":"2019-12-15T00:00:00Z","abstract":[{"text":"The aim of this short paper is to offer a complete characterization of all (not necessarily surjective) isometric embeddings of the Wasserstein space Wp(X), where S is a countable discrete metric space and 0<p<∞ is any parameter value. Roughly speaking, we will prove that any isometric embedding can be described by a special kind of X×(0,1]-indexed family of nonnegative finite measures. Our result implies that a typical non-surjective isometric embedding of Wp(X) splits mass and does not preserve the shape of measures. In order to stress that the lack of surjectivity is what makes things challenging, we will prove alternatively that Wp(X) is isometrically rigid for all 0<p<∞.","lang":"eng"}],"publication_status":"published"},{"quality_controlled":"1","citation":{"ama":"Geher GP, Titkos T, Virosztek D. Dirac masses and isometric rigidity. In: <i>Kyoto RIMS Kôkyûroku</i>. Vol 2125. Research Institute for Mathematical Sciences, Kyoto University; 2019:34-41.","ista":"Geher GP, Titkos T, Virosztek D. 2019. Dirac masses and isometric rigidity. Kyoto RIMS Kôkyûroku. Research on isometries as preserver problems and related topics vol. 2125, 34–41.","mla":"Geher, Gyorgy Pal, et al. “Dirac Masses and Isometric Rigidity.” <i>Kyoto RIMS Kôkyûroku</i>, vol. 2125, Research Institute for Mathematical Sciences, Kyoto University, 2019, pp. 34–41.","ieee":"G. P. Geher, T. Titkos, and D. Virosztek, “Dirac masses and isometric rigidity,” in <i>Kyoto RIMS Kôkyûroku</i>, Kyoto, Japan, 2019, vol. 2125, pp. 34–41.","chicago":"Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Dirac Masses and Isometric Rigidity.” In <i>Kyoto RIMS Kôkyûroku</i>, 2125:34–41. Research Institute for Mathematical Sciences, Kyoto University, 2019.","apa":"Geher, G. P., Titkos, T., &#38; Virosztek, D. (2019). Dirac masses and isometric rigidity. In <i>Kyoto RIMS Kôkyûroku</i> (Vol. 2125, pp. 34–41). Kyoto, Japan: Research Institute for Mathematical Sciences, Kyoto University.","short":"G.P. Geher, T. Titkos, D. Virosztek, in:, Kyoto RIMS Kôkyûroku, Research Institute for Mathematical Sciences, Kyoto University, 2019, pp. 34–41."},"author":[{"first_name":"Gyorgy Pal","last_name":"Geher","full_name":"Geher, Gyorgy Pal"},{"last_name":"Titkos","first_name":"Tamas","full_name":"Titkos, Tamas"},{"full_name":"Virosztek, Daniel","first_name":"Daniel","orcid":"0000-0003-1109-5511","last_name":"Virosztek","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"_id":"7035","intvolume":"      2125","publisher":"Research Institute for Mathematical Sciences, Kyoto University","type":"conference","OA_place":"repository","page":"34-41","title":"Dirac masses and isometric rigidity","volume":2125,"year":"2019","publication":"Kyoto RIMS Kôkyûroku","project":[{"grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme"}],"acknowledgement":"This paper is part of a long term collaboration investigating the isometric structure of Wasserstein\r\nspaces. The authors would like to thank the warm hospitality and generosity of László Erdós and his\r\ngroup at Institute of Science and Technology Austria.\r\nT. Titkos wants to thank Oriental Business and Innovation Center ‐ OBIC for providing financial\r\nsupport to participate in the symposium at the Kyoto RIMS.\r\nGy. P. Gehér was supported by the Leverhulme Trust Early Career Fellowship (ECF‐2018‐125),\r\nand also by the Hungarian National Research, Development and Innovation Office (K115383). T.\r\nTitkos was supported by the Hungarian National Research, Development and Innovation Office‐ NKFIH\r\n(PD128374), by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the\r\nUNKP‐18‐4‐BGE‐3 New National Excellence Program of the Ministry of Human Capacities. D. Virosztek\r\nwas supported by the ISTFELLOW program of the Institute of Science and Technology Austria (project\r\ncode IC1027FELL01 ) and partially supported by the Hungarian National Research, Development and\r\nInnovation Office NKFIH (grant no. K124152 and grant no. KH129601)","date_created":"2019-11-18T15:39:53Z","article_processing_charge":"No","conference":{"name":"Research on isometries as preserver problems and related topics","location":"Kyoto, Japan","end_date":"2019-01-30","start_date":"2019-01-28"},"department":[{"_id":"LaEr"}],"date_updated":"2025-06-30T09:55:30Z","oa_version":"Submitted Version","language":[{"iso":"eng"}],"ec_funded":1,"oa":1,"day":"30","corr_author":"1","publication_status":"published","abstract":[{"lang":"eng","text":"The aim of this short note is to expound one particular issue that was discussed during the talk [10] given at the symposium ”Researches on isometries as preserver problems and related topics” at Kyoto RIMS. That is,  the role of Dirac masses by  describing  the  isometry group of various metric spaces  of probability  measures.   This  article  is  of  survey  character,  and  it  does  not  contain  any  essentially  new results.From an isometric point of view, in some cases, metric spaces of measures are similar to C(K)-type function  spaces.   Similarity  means  here  that  their  isometries  are  driven  by  some  nice  transformations of  the  underlying  space.   Of  course,  it  depends  on  the  particular  choice  of  the  metric  how  nice  these transformations should be.  Sometimes, as we will see, being a homeomorphism is enough to generate an isometry.  But sometimes we need more:  the transformation must preserve the underlying distance as well.  Statements claiming that isometries in questions are necessarily induced by homeomorphisms are called Banach-Stone-type results, while results asserting that the underlying transformation is necessarily an isometry are termed as isometric rigidity results.As  Dirac  masses  can  be  considered  as  building  bricks  of  the  set  of  all  Borel  measures,  a  natural question arises:Is it enough to understand how an isometry acts on the set of Dirac masses?  Does this action extend uniquely to all measures?In what follows, we will thoroughly investigate this question."}],"date_published":"2019-01-30T00:00:00Z","status":"public","OA_type":"green","month":"01","main_file_link":[{"open_access":"1","url":"http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/2125.html"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"article_type":"original","title":"Limit law of a second class particle in TASEP with non-random initial condition","external_id":{"isi":["000487763200001"],"arxiv":["1710.02323"]},"volume":55,"year":"2019","publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","project":[{"name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804"},{"call_identifier":"H2020","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"page":"1203-1225","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"date_created":"2018-12-11T11:44:29Z","article_processing_charge":"No","publication_identifier":{"issn":["0246-0203"]},"author":[{"first_name":"Patrick","last_name":"Ferrari","full_name":"Ferrari, Patrick"},{"full_name":"Ghosal, Promit","last_name":"Ghosal","first_name":"Promit"},{"first_name":"Peter","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","last_name":"Nejjar","full_name":"Nejjar, Peter"}],"_id":"72","scopus_import":"1","quality_controlled":"1","citation":{"apa":"Ferrari, P., Ghosal, P., &#38; Nejjar, P. (2019). Limit law of a second class particle in TASEP with non-random initial condition. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/18-AIHP916\">https://doi.org/10.1214/18-AIHP916</a>","short":"P. Ferrari, P. Ghosal, P. Nejjar, Annales de l’institut Henri Poincare (B) Probability and Statistics 55 (2019) 1203–1225.","chicago":"Ferrari, Patrick, Promit Ghosal, and Peter Nejjar. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics, 2019. <a href=\"https://doi.org/10.1214/18-AIHP916\">https://doi.org/10.1214/18-AIHP916</a>.","ista":"Ferrari P, Ghosal P, Nejjar P. 2019. Limit law of a second class particle in TASEP with non-random initial condition. Annales de l’institut Henri Poincare (B) Probability and Statistics. 55(3), 1203–1225.","ieee":"P. Ferrari, P. Ghosal, and P. Nejjar, “Limit law of a second class particle in TASEP with non-random initial condition,” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol. 55, no. 3. Institute of Mathematical Statistics, pp. 1203–1225, 2019.","mla":"Ferrari, Patrick, et al. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol. 55, no. 3, Institute of Mathematical Statistics, 2019, pp. 1203–25, doi:<a href=\"https://doi.org/10.1214/18-AIHP916\">10.1214/18-AIHP916</a>.","ama":"Ferrari P, Ghosal P, Nejjar P. Limit law of a second class particle in TASEP with non-random initial condition. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. 2019;55(3):1203-1225. doi:<a href=\"https://doi.org/10.1214/18-AIHP916\">10.1214/18-AIHP916</a>"},"type":"journal_article","isi":1,"intvolume":"        55","publisher":"Institute of Mathematical Statistics","date_published":"2019-09-25T00:00:00Z","status":"public","abstract":[{"lang":"eng","text":"We consider the totally asymmetric simple exclusion process (TASEP) with non-random initial condition having density ρ on ℤ− and λ on ℤ+, and a second class particle initially at the origin. For ρ&lt;λ, there is a shock and the second class particle moves with speed 1−λ−ρ. For large time t, we show that the position of the second class particle fluctuates on a t1/3 scale and determine its limiting law. We also obtain the limiting distribution of the number of steps made by the second class particle until time t."}],"publication_status":"published","doi":"10.1214/18-AIHP916","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"09","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1710.02323"}],"language":[{"iso":"eng"}],"oa":1,"ec_funded":1,"issue":"3","oa_version":"Preprint","date_updated":"2025-04-14T07:27:49Z","arxiv":1,"day":"25"},{"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","doi":"10.1214/18-aihp888","month":"02","main_file_link":[{"url":"https://arxiv.org/abs/1704.05224","open_access":"1"}],"date_published":"2019-02-01T00:00:00Z","status":"public","abstract":[{"lang":"eng","text":"We compare finite rank perturbations of the following three ensembles of complex rectangular random matrices: First, a generalised Wishart ensemble with one random and two fixed correlation matrices introduced by Borodin and Péché, second, the product of two independent random matrices where one has correlated entries, and third, the case when the two random matrices become also coupled through a fixed matrix. The singular value statistics of all three ensembles is shown to be determinantal and we derive double contour integral representations for their respective kernels. Three different kernels are found in the limit of infinite matrix dimension at the origin of the spectrum. They depend on finite rank perturbations of the correlation and coupling matrices and are shown to be integrable. The first kernel (I) is found for two independent matrices from the second, and two weakly coupled matrices from the third ensemble. It generalises the Meijer G-kernel for two independent and uncorrelated matrices. The third kernel (III) is obtained for the generalised Wishart ensemble and for two strongly coupled matrices. It further generalises the perturbed Bessel kernel of Desrosiers and Forrester. Finally, kernel (II), found for the ensemble of two coupled matrices, provides an interpolation between the kernels (I) and (III), generalising previous findings of part of the authors."}],"publication_status":"published","day":"01","oa":1,"language":[{"iso":"eng"}],"date_updated":"2023-09-06T14:58:39Z","oa_version":"Preprint","issue":"1","arxiv":1,"department":[{"_id":"LaEr"}],"article_processing_charge":"No","date_created":"2020-01-30T10:36:50Z","publication_identifier":{"issn":["0246-0203"]},"volume":55,"external_id":{"arxiv":["1704.05224"],"isi":["000456070200013"]},"article_type":"original","title":"Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles","publication":"Annales de l'Institut Henri Poincaré, Probabilités et Statistiques","year":"2019","page":"441-479","isi":1,"type":"journal_article","intvolume":"        55","publisher":"Institute of Mathematical Statistics","_id":"7423","author":[{"full_name":"Akemann, Gernot","first_name":"Gernot","last_name":"Akemann"},{"full_name":"Checinski, Tomasz","last_name":"Checinski","first_name":"Tomasz"},{"id":"2F947E34-F248-11E8-B48F-1D18A9856A87","last_name":"Liu","first_name":"Dangzheng","full_name":"Liu, Dangzheng"},{"full_name":"Strahov, Eugene","first_name":"Eugene","last_name":"Strahov"}],"quality_controlled":"1","citation":{"short":"G. Akemann, T. Checinski, D. Liu, E. Strahov, Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55 (2019) 441–479.","apa":"Akemann, G., Checinski, T., Liu, D., &#38; Strahov, E. (2019). Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles. <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/18-aihp888\">https://doi.org/10.1214/18-aihp888</a>","chicago":"Akemann, Gernot, Tomasz Checinski, Dangzheng Liu, and Eugene Strahov. “Finite Rank Perturbations in Products of Coupled Random Matrices: From One Correlated to Two Wishart Ensembles.” <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>. Institute of Mathematical Statistics, 2019. <a href=\"https://doi.org/10.1214/18-aihp888\">https://doi.org/10.1214/18-aihp888</a>.","mla":"Akemann, Gernot, et al. “Finite Rank Perturbations in Products of Coupled Random Matrices: From One Correlated to Two Wishart Ensembles.” <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>, vol. 55, no. 1, Institute of Mathematical Statistics, 2019, pp. 441–79, doi:<a href=\"https://doi.org/10.1214/18-aihp888\">10.1214/18-aihp888</a>.","ista":"Akemann G, Checinski T, Liu D, Strahov E. 2019. Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. 55(1), 441–479.","ieee":"G. Akemann, T. Checinski, D. Liu, and E. Strahov, “Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles,” <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>, vol. 55, no. 1. Institute of Mathematical Statistics, pp. 441–479, 2019.","ama":"Akemann G, Checinski T, Liu D, Strahov E. Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles. <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>. 2019;55(1):441-479. doi:<a href=\"https://doi.org/10.1214/18-aihp888\">10.1214/18-aihp888</a>"}},{"day":"01","corr_author":"1","arxiv":1,"oa_version":"Preprint","date_updated":"2025-04-15T06:50:00Z","oa":1,"language":[{"iso":"eng"}],"ec_funded":1,"main_file_link":[{"url":"https://arxiv.org/abs/1712.05324","open_access":"1"}],"month":"09","doi":"10.1016/j.laa.2018.03.002","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","abstract":[{"lang":"eng","text":"We investigate the quantum Jensen divergences from the viewpoint of joint convexity. It turns out that the set of the functions which generate jointly convex quantum Jensen divergences on positive matrices coincides with the Matrix Entropy Class which has been introduced by Chen and Tropp quite recently."}],"status":"public","date_published":"2019-09-01T00:00:00Z","publisher":"Elsevier","intvolume":"       576","type":"journal_article","isi":1,"citation":{"apa":"Virosztek, D. (2019). Jointly convex quantum Jensen divergences. <i>Linear Algebra and Its Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.laa.2018.03.002\">https://doi.org/10.1016/j.laa.2018.03.002</a>","short":"D. Virosztek, Linear Algebra and Its Applications 576 (2019) 67–78.","chicago":"Virosztek, Daniel. “Jointly Convex Quantum Jensen Divergences.” <i>Linear Algebra and Its Applications</i>. Elsevier, 2019. <a href=\"https://doi.org/10.1016/j.laa.2018.03.002\">https://doi.org/10.1016/j.laa.2018.03.002</a>.","ieee":"D. Virosztek, “Jointly convex quantum Jensen divergences,” <i>Linear Algebra and Its Applications</i>, vol. 576. Elsevier, pp. 67–78, 2019.","ista":"Virosztek D. 2019. Jointly convex quantum Jensen divergences. Linear Algebra and Its Applications. 576, 67–78.","mla":"Virosztek, Daniel. “Jointly Convex Quantum Jensen Divergences.” <i>Linear Algebra and Its Applications</i>, vol. 576, Elsevier, 2019, pp. 67–78, doi:<a href=\"https://doi.org/10.1016/j.laa.2018.03.002\">10.1016/j.laa.2018.03.002</a>.","ama":"Virosztek D. Jointly convex quantum Jensen divergences. <i>Linear Algebra and Its Applications</i>. 2019;576:67-78. doi:<a href=\"https://doi.org/10.1016/j.laa.2018.03.002\">10.1016/j.laa.2018.03.002</a>"},"quality_controlled":"1","scopus_import":"1","author":[{"id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","last_name":"Virosztek","orcid":"0000-0003-1109-5511","first_name":"Daniel","full_name":"Virosztek, Daniel"}],"_id":"405","date_created":"2018-12-11T11:46:17Z","acknowledgement":"The author was supported by the ISTFELLOW program of the Institute of Science and Technology Austria (project code IC1027FELL01) and partially supported by the Hungarian National Research, Development and Innovation Office – NKFIH (grant no. K124152)","article_processing_charge":"No","department":[{"_id":"LaEr"}],"page":"67-78","publist_id":"7424","year":"2019","project":[{"grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme"}],"publication":"Linear Algebra and Its Applications","external_id":{"isi":["000470955300005"],"arxiv":["1712.05324"]},"article_type":"original","title":"Jointly convex quantum Jensen divergences","volume":576},{"day":"01","corr_author":"1","license":"https://creativecommons.org/licenses/by/4.0/","file":[{"date_updated":"2020-07-14T12:46:26Z","creator":"dernst","access_level":"open_access","content_type":"application/pdf","relation":"main_file","date_created":"2018-12-17T16:12:08Z","file_id":"5720","checksum":"f9354fa5c71f9edd17132588f0dc7d01","file_name":"2018_ProbTheory_Ajanki.pdf","file_size":1201840}],"date_updated":"2026-04-03T09:46:51Z","oa_version":"Published Version","issue":"1-2","oa":1,"language":[{"iso":"eng"}],"ec_funded":1,"month":"02","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","doi":"10.1007/s00440-018-0835-z","ddc":["510"],"abstract":[{"text":"We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay but are otherwise of general form. The key novelty is the detailed stability analysis of the corresponding matrix valued Dyson equation whose solution is the deterministic limit of the resolvent.","lang":"eng"}],"publication_status":"published","date_published":"2019-02-01T00:00:00Z","status":"public","intvolume":"       173","publisher":"Springer","isi":1,"type":"journal_article","quality_controlled":"1","scopus_import":"1","has_accepted_license":"1","citation":{"chicago":"Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Stability of the Matrix Dyson Equation and Random Matrices with Correlations.” <i>Probability Theory and Related Fields</i>. Springer, 2019. <a href=\"https://doi.org/10.1007/s00440-018-0835-z\">https://doi.org/10.1007/s00440-018-0835-z</a>.","apa":"Ajanki, O. H., Erdös, L., &#38; Krüger, T. H. (2019). Stability of the matrix Dyson equation and random matrices with correlations. <i>Probability Theory and Related Fields</i>. Springer. <a href=\"https://doi.org/10.1007/s00440-018-0835-z\">https://doi.org/10.1007/s00440-018-0835-z</a>","short":"O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields 173 (2019) 293–373.","ama":"Ajanki OH, Erdös L, Krüger TH. Stability of the matrix Dyson equation and random matrices with correlations. <i>Probability Theory and Related Fields</i>. 2019;173(1-2):293–373. doi:<a href=\"https://doi.org/10.1007/s00440-018-0835-z\">10.1007/s00440-018-0835-z</a>","mla":"Ajanki, Oskari H., et al. “Stability of the Matrix Dyson Equation and Random Matrices with Correlations.” <i>Probability Theory and Related Fields</i>, vol. 173, no. 1–2, Springer, 2019, pp. 293–373, doi:<a href=\"https://doi.org/10.1007/s00440-018-0835-z\">10.1007/s00440-018-0835-z</a>.","ista":"Ajanki OH, Erdös L, Krüger TH. 2019. Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. 173(1–2), 293–373.","ieee":"O. H. Ajanki, L. Erdös, and T. H. Krüger, “Stability of the matrix Dyson equation and random matrices with correlations,” <i>Probability Theory and Related Fields</i>, vol. 173, no. 1–2. Springer, pp. 293–373, 2019."},"_id":"429","file_date_updated":"2020-07-14T12:46:26Z","author":[{"full_name":"Ajanki, Oskari H","first_name":"Oskari H","id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87","last_name":"Ajanki"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László"},{"full_name":"Krüger, Torben H","first_name":"Torben H","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297"}],"article_processing_charge":"Yes (via OA deal)","date_created":"2018-12-11T11:46:25Z","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).\r\n","publication_identifier":{"issn":["0178-8051"],"eissn":["1432-2064"]},"department":[{"_id":"LaEr"}],"publist_id":"7394","page":"293–373","volume":173,"external_id":{"isi":["000459396500007"]},"article_type":"original","title":"Stability of the matrix Dyson equation and random matrices with correlations","project":[{"name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"publication":"Probability Theory and Related Fields","year":"2019"},{"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","doi":"10.15479/AT:ISTA:th6179","supervisor":[{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"}],"month":"03","date_published":"2019-03-18T00:00:00Z","status":"public","ddc":["515","519"],"abstract":[{"text":"In the first part of this thesis we consider large random matrices with arbitrary expectation and a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent in the bulk and edge regime. The main novel tool is a systematic diagrammatic control of a multivariate cumulant expansion.\r\nIn the second part we consider Wigner-type matrices and show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are uni- versal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner- Dyson-Mehta universality conjecture for the last remaining universality type. Our analysis holds not only for exact cusps, but approximate cusps as well, where an ex- tended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp, and extend the fast relaxation to equilibrium of the Dyson Brow- nian motion to the cusp regime.\r\nIn the third and final part we explore the entrywise linear statistics of Wigner ma- trices and identify the fluctuations for a large class of test functions with little regularity. This enables us to study the rectangular Young diagram obtained from the interlacing eigenvalues of the random matrix and its minor, and we find that, despite having the same limit, the fluctuations differ from those of the algebraic Young tableaux equipped with the Plancharel measure.","lang":"eng"}],"publication_status":"published","corr_author":"1","file":[{"checksum":"6926f66f28079a81c4937e3764be00fc","file_id":"6180","date_created":"2019-03-28T08:53:52Z","file_name":"2019_Schroeder_Thesis.tar.gz","file_size":7104482,"access_level":"closed","creator":"dernst","date_updated":"2020-07-14T12:47:21Z","relation":"source_file","content_type":"application/x-gzip"},{"file_name":"2019_Schroeder_Thesis.pdf","file_size":4228794,"date_created":"2019-03-28T08:53:52Z","file_id":"6181","checksum":"7d0ebb8d1207e89768cdd497a5bf80fb","content_type":"application/pdf","relation":"main_file","date_updated":"2020-07-14T12:47:21Z","creator":"dernst","access_level":"open_access"}],"day":"18","language":[{"iso":"eng"}],"oa":1,"ec_funded":1,"oa_version":"Published Version","alternative_title":["ISTA Thesis"],"date_updated":"2026-04-08T13:55:03Z","department":[{"_id":"LaEr"}],"article_processing_charge":"No","date_created":"2019-03-28T08:58:59Z","publication_identifier":{"issn":["2663-337X"]},"title":"From Dyson to Pearcey: Universal statistics in random matrix theory","project":[{"call_identifier":"FP7","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems"}],"year":"2019","degree_awarded":"PhD","OA_place":"publisher","page":"375","related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"6184"},{"id":"6186","status":"public","relation":"part_of_dissertation"},{"id":"6185","status":"public","relation":"part_of_dissertation"},{"status":"public","id":"1012","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"1144","status":"public"},{"relation":"part_of_dissertation","status":"public","id":"6182"}]},"type":"dissertation","publisher":"Institute of Science and Technology Austria","file_date_updated":"2020-07-14T12:47:21Z","_id":"6179","author":[{"orcid":"0000-0002-2904-1856","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","full_name":"Schröder, Dominik J"}],"has_accepted_license":"1","citation":{"mla":"Schröder, Dominik J. <i>From Dyson to Pearcey: Universal Statistics in Random Matrix Theory</i>. Institute of Science and Technology Austria, 2019, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:th6179\">10.15479/AT:ISTA:th6179</a>.","ista":"Schröder DJ. 2019. From Dyson to Pearcey: Universal statistics in random matrix theory. Institute of Science and Technology Austria.","ieee":"D. J. Schröder, “From Dyson to Pearcey: Universal statistics in random matrix theory,” Institute of Science and Technology Austria, 2019.","ama":"Schröder DJ. From Dyson to Pearcey: Universal statistics in random matrix theory. 2019. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:th6179\">10.15479/AT:ISTA:th6179</a>","short":"D.J. Schröder, From Dyson to Pearcey: Universal Statistics in Random Matrix Theory, Institute of Science and Technology Austria, 2019.","apa":"Schröder, D. J. (2019). <i>From Dyson to Pearcey: Universal statistics in random matrix theory</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:th6179\">https://doi.org/10.15479/AT:ISTA:th6179</a>","chicago":"Schröder, Dominik J. “From Dyson to Pearcey: Universal Statistics in Random Matrix Theory.” Institute of Science and Technology Austria, 2019. <a href=\"https://doi.org/10.15479/AT:ISTA:th6179\">https://doi.org/10.15479/AT:ISTA:th6179</a>."}},{"publication_status":"published","abstract":[{"text":"We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the recent result of Ajanki et al. [‘Stability of the matrix Dyson equation and random matrices with correlations’, Probab. Theory Related Fields 173(1–2) (2019), 293–373] to allow slow correlation decay and arbitrary expectation. The main novel tool is\r\na systematic diagrammatic control of a multivariate cumulant expansion.","lang":"eng"}],"ddc":["510"],"status":"public","date_published":"2019-03-26T00:00:00Z","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"month":"03","doi":"10.1017/fms.2019.2","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","arxiv":1,"date_updated":"2026-04-08T13:55:03Z","oa_version":"Published Version","language":[{"iso":"eng"}],"ec_funded":1,"oa":1,"day":"26","file":[{"file_size":1520344,"file_name":"2019_Forum_Erdoes.pdf","file_id":"6883","date_created":"2019-09-17T14:24:13Z","checksum":"933a472568221c73b2c3ce8c87bf6d15","relation":"main_file","content_type":"application/pdf","date_updated":"2020-07-14T12:47:22Z","access_level":"open_access","creator":"dernst"}],"corr_author":"1","related_material":{"record":[{"relation":"dissertation_contains","id":"6179","status":"public"}]},"year":"2019","publication":"Forum of Mathematics, Sigma","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804"}],"external_id":{"arxiv":["1705.10661"],"isi":["000488847100001"]},"article_type":"original","title":"Random matrices with slow correlation decay","volume":7,"publication_identifier":{"eissn":["2050-5094"]},"date_created":"2019-03-28T09:05:23Z","article_processing_charge":"No","department":[{"_id":"LaEr"}],"citation":{"chicago":"Erdös, László, Torben H Krüger, and Dominik J Schröder. “Random Matrices with Slow Correlation Decay.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2019. <a href=\"https://doi.org/10.1017/fms.2019.2\">https://doi.org/10.1017/fms.2019.2</a>.","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Forum of Mathematics, Sigma 7 (2019).","apa":"Erdös, L., Krüger, T. H., &#38; Schröder, D. J. (2019). Random matrices with slow correlation decay. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2019.2\">https://doi.org/10.1017/fms.2019.2</a>","ama":"Erdös L, Krüger TH, Schröder DJ. Random matrices with slow correlation decay. <i>Forum of Mathematics, Sigma</i>. 2019;7. doi:<a href=\"https://doi.org/10.1017/fms.2019.2\">10.1017/fms.2019.2</a>","ista":"Erdös L, Krüger TH, Schröder DJ. 2019. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 7, e8.","ieee":"L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation decay,” <i>Forum of Mathematics, Sigma</i>, vol. 7. Cambridge University Press, 2019.","mla":"Erdös, László, et al. “Random Matrices with Slow Correlation Decay.” <i>Forum of Mathematics, Sigma</i>, vol. 7, e8, Cambridge University Press, 2019, doi:<a href=\"https://doi.org/10.1017/fms.2019.2\">10.1017/fms.2019.2</a>."},"has_accepted_license":"1","article_number":"e8","scopus_import":"1","quality_controlled":"1","author":[{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László"},{"orcid":"0000-0002-4821-3297","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H","full_name":"Krüger, Torben H"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","first_name":"Dominik J"}],"file_date_updated":"2020-07-14T12:47:22Z","_id":"6182","publisher":"Cambridge University Press","intvolume":"         7","type":"journal_article","isi":1},{"day":"12","language":[{"iso":"eng"}],"ec_funded":1,"oa":1,"oa_version":"Preprint","date_updated":"2026-04-08T13:55:02Z","issue":"4","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.2140/paa.2019.1.615","month":"10","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1811.04055"}],"date_published":"2019-10-12T00:00:00Z","status":"public","publication_status":"published","abstract":[{"text":"We prove that the local eigenvalue statistics of real symmetric Wigner-type\r\nmatrices near the cusp points of the eigenvalue density are universal. Together\r\nwith the companion paper [arXiv:1809.03971], which proves the same result for\r\nthe complex Hermitian symmetry class, this completes the last remaining case of\r\nthe Wigner-Dyson-Mehta universality conjecture after bulk and edge\r\nuniversalities have been established in the last years. We extend the recent\r\nDyson Brownian motion analysis at the edge [arXiv:1712.03881] to the cusp\r\nregime using the optimal local law from [arXiv:1809.03971] and the accurate\r\nlocal shape analysis of the density from [arXiv:1506.05095, arXiv:1804.07752].\r\nWe also present a PDE-based method to improve the estimate on eigenvalue\r\nrigidity via the maximum principle of the heat flow related to the Dyson\r\nBrownian motion.","lang":"eng"}],"type":"journal_article","intvolume":"         1","publisher":"MSP","_id":"6186","author":[{"full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","orcid":"0000-0002-4901-7992"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","last_name":"Krüger","first_name":"Torben H"},{"first_name":"Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"quality_controlled":"1","scopus_import":"1","citation":{"mla":"Cipolloni, Giorgio, et al. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” <i>Pure and Applied Analysis </i>, vol. 1, no. 4, MSP, 2019, pp. 615–707, doi:<a href=\"https://doi.org/10.2140/paa.2019.1.615\">10.2140/paa.2019.1.615</a>.","ieee":"G. Cipolloni, L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices, II: The real symmetric case,” <i>Pure and Applied Analysis </i>, vol. 1, no. 4. MSP, pp. 615–707, 2019.","ista":"Cipolloni G, Erdös L, Krüger TH, Schröder DJ. 2019. Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . 1(4), 615–707.","ama":"Cipolloni G, Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices, II: The real symmetric case. <i>Pure and Applied Analysis </i>. 2019;1(4):615–707. doi:<a href=\"https://doi.org/10.2140/paa.2019.1.615\">10.2140/paa.2019.1.615</a>","short":"G. Cipolloni, L. Erdös, T.H. Krüger, D.J. Schröder, Pure and Applied Analysis  1 (2019) 615–707.","apa":"Cipolloni, G., Erdös, L., Krüger, T. H., &#38; Schröder, D. J. (2019). Cusp universality for random matrices, II: The real symmetric case. <i>Pure and Applied Analysis </i>. MSP. <a href=\"https://doi.org/10.2140/paa.2019.1.615\">https://doi.org/10.2140/paa.2019.1.615</a>","chicago":"Cipolloni, Giorgio, László Erdös, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” <i>Pure and Applied Analysis </i>. MSP, 2019. <a href=\"https://doi.org/10.2140/paa.2019.1.615\">https://doi.org/10.2140/paa.2019.1.615</a>."},"department":[{"_id":"LaEr"}],"article_processing_charge":"No","date_created":"2019-03-28T10:21:17Z","publication_identifier":{"issn":["2578-5893"],"eissn":["2578-5885"]},"volume":1,"article_type":"original","title":"Cusp universality for random matrices, II: The real symmetric case","external_id":{"arxiv":["1811.04055"]},"publication":"Pure and Applied Analysis ","project":[{"name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7"},{"grant_number":"665385","call_identifier":"H2020","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"year":"2019","page":"615–707","related_material":{"record":[{"status":"public","id":"6179","relation":"dissertation_contains"}]}},{"issue":"2","date_updated":"2026-04-08T14:11:36Z","oa_version":"Preprint","arxiv":1,"oa":1,"language":[{"iso":"eng"}],"ec_funded":1,"day":"01","publication_status":"published","abstract":[{"lang":"eng","text":"For a general class of large non-Hermitian random block matrices X we prove that there are no eigenvalues away from a deterministic set with very high probability. This set is obtained from the Dyson equation of the Hermitization of X as the self-consistent approximation of the pseudospectrum. We demonstrate that the analysis of the matrix Dyson equation from (Probab. Theory Related Fields (2018)) offers a unified treatment of many structured matrix ensembles."}],"date_published":"2019-05-01T00:00:00Z","status":"public","month":"05","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1706.08343"}],"doi":"10.1214/18-AIHP894","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","scopus_import":"1","citation":{"ama":"Alt J, Erdös L, Krüger TH, Nemish Y. Location of the spectrum of Kronecker random matrices. <i>Annales de l’institut Henri Poincare</i>. 2019;55(2):661-696. doi:<a href=\"https://doi.org/10.1214/18-AIHP894\">10.1214/18-AIHP894</a>","ieee":"J. Alt, L. Erdös, T. H. Krüger, and Y. Nemish, “Location of the spectrum of Kronecker random matrices,” <i>Annales de l’institut Henri Poincare</i>, vol. 55, no. 2. Institut Henri Poincaré, pp. 661–696, 2019.","mla":"Alt, Johannes, et al. “Location of the Spectrum of Kronecker Random Matrices.” <i>Annales de l’institut Henri Poincare</i>, vol. 55, no. 2, Institut Henri Poincaré, 2019, pp. 661–96, doi:<a href=\"https://doi.org/10.1214/18-AIHP894\">10.1214/18-AIHP894</a>.","ista":"Alt J, Erdös L, Krüger TH, Nemish Y. 2019. Location of the spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare. 55(2), 661–696.","chicago":"Alt, Johannes, László Erdös, Torben H Krüger, and Yuriy Nemish. “Location of the Spectrum of Kronecker Random Matrices.” <i>Annales de l’institut Henri Poincare</i>. Institut Henri Poincaré, 2019. <a href=\"https://doi.org/10.1214/18-AIHP894\">https://doi.org/10.1214/18-AIHP894</a>.","short":"J. Alt, L. Erdös, T.H. Krüger, Y. Nemish, Annales de l’institut Henri Poincare 55 (2019) 661–696.","apa":"Alt, J., Erdös, L., Krüger, T. H., &#38; Nemish, Y. (2019). Location of the spectrum of Kronecker random matrices. <i>Annales de l’institut Henri Poincare</i>. Institut Henri Poincaré. <a href=\"https://doi.org/10.1214/18-AIHP894\">https://doi.org/10.1214/18-AIHP894</a>"},"author":[{"first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","last_name":"Alt","full_name":"Alt, Johannes"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László"},{"first_name":"Torben H","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H"},{"full_name":"Nemish, Yuriy","first_name":"Yuriy","last_name":"Nemish","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7327-856X"}],"_id":"6240","intvolume":"        55","publisher":"Institut Henri Poincaré","type":"journal_article","isi":1,"page":"661-696","related_material":{"record":[{"status":"public","id":"149","relation":"dissertation_contains"}]},"external_id":{"isi":["000467793600003"],"arxiv":["1706.08343"]},"title":"Location of the spectrum of Kronecker random matrices","volume":55,"year":"2019","publication":"Annales de l'institut Henri Poincare","project":[{"name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804"}],"date_created":"2019-04-08T14:05:04Z","article_processing_charge":"No","publication_identifier":{"issn":["0246-0203"]},"department":[{"_id":"LaEr"}]},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1802.03305"}],"month":"06","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.14232/actasm-018-753-y","abstract":[{"text":"Borel probability measures living on metric spaces are fundamental\r\nmathematical objects. There are several meaningful distance functions that make the collection of the probability measures living on a certain space a metric space. We are interested in the description of the structure of the isometries of such metric spaces. We overview some of the recent results of the topic and we also provide some new ones concerning the Wasserstein distance. More specifically, we consider the space of all Borel probability measures on the unit sphere of a Euclidean space endowed with the Wasserstein metric W_p for arbitrary p &gt;= 1, and we show that the action of a Wasserstein isometry on the set of Dirac measures is induced by an isometry of the underlying unit sphere.","lang":"eng"}],"publication_status":"published","status":"public","date_published":"2018-06-04T00:00:00Z","day":"04","arxiv":1,"date_updated":"2025-04-15T06:50:21Z","oa_version":"Preprint","issue":"1-2","language":[{"iso":"eng"}],"oa":1,"ec_funded":1,"publication_identifier":{"issn":["0001-6969"],"eissn":["2064-8316"]},"article_processing_charge":"No","acknowledgement":"The author was supported by the ISTFELLOW program of the Institute of Science and Technol- ogy Austria (project code IC1027FELL01) and partially supported by the Hungarian National Research, Development and Innovation Office, NKFIH (grant no. K124152).","date_created":"2018-12-11T11:45:36Z","department":[{"_id":"LaEr"}],"publist_id":"7615","page":"65 - 80","project":[{"grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme"}],"publication":"Acta Scientiarum Mathematicarum","year":"2018","volume":84,"article_type":"original","title":"Maps on probability measures preserving certain distances - a survey and some new results","external_id":{"arxiv":["1802.03305"]},"publisher":"Springer Nature","intvolume":"        84","type":"journal_article","citation":{"chicago":"Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances - a Survey and Some New Results.” <i>Acta Scientiarum Mathematicarum</i>. Springer Nature, 2018. <a href=\"https://doi.org/10.14232/actasm-018-753-y\">https://doi.org/10.14232/actasm-018-753-y</a>.","apa":"Virosztek, D. (2018). Maps on probability measures preserving certain distances - a survey and some new results. <i>Acta Scientiarum Mathematicarum</i>. Springer Nature. <a href=\"https://doi.org/10.14232/actasm-018-753-y\">https://doi.org/10.14232/actasm-018-753-y</a>","short":"D. Virosztek, Acta Scientiarum Mathematicarum 84 (2018) 65–80.","ama":"Virosztek D. Maps on probability measures preserving certain distances - a survey and some new results. <i>Acta Scientiarum Mathematicarum</i>. 2018;84(1-2):65-80. doi:<a href=\"https://doi.org/10.14232/actasm-018-753-y\">10.14232/actasm-018-753-y</a>","mla":"Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances - a Survey and Some New Results.” <i>Acta Scientiarum Mathematicarum</i>, vol. 84, no. 1–2, Springer Nature, 2018, pp. 65–80, doi:<a href=\"https://doi.org/10.14232/actasm-018-753-y\">10.14232/actasm-018-753-y</a>.","ieee":"D. Virosztek, “Maps on probability measures preserving certain distances - a survey and some new results,” <i>Acta Scientiarum Mathematicarum</i>, vol. 84, no. 1–2. Springer Nature, pp. 65–80, 2018.","ista":"Virosztek D. 2018. Maps on probability measures preserving certain distances - a survey and some new results. Acta Scientiarum Mathematicarum. 84(1–2), 65–80."},"quality_controlled":"1","scopus_import":"1","_id":"284","author":[{"full_name":"Virosztek, Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","last_name":"Virosztek","orcid":"0000-0003-1109-5511","first_name":"Daniel"}]},{"doi":"10.1137/17M1143125","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","month":"01","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.01546"}],"date_published":"2018-01-01T00:00:00Z","status":"public","publication_status":"published","abstract":[{"lang":"eng","text":"We consider large random matrices X with centered, independent entries but possibly di erent variances. We compute the normalized trace of f(X)g(X∗) for f, g functions analytic on the spectrum of X. We use these results to compute the long time asymptotics for systems of coupled di erential equations with random coe cients. We show that when the coupling is critical, the norm squared of the solution decays like t−1/2."}],"day":"01","ec_funded":1,"oa":1,"language":[{"iso":"eng"}],"issue":"3","date_updated":"2025-04-15T08:05:02Z","oa_version":"Published Version","arxiv":1,"department":[{"_id":"LaEr"}],"acknowledgement":"The work of the second author was also partially supported by the Hausdorff Center of Mathematics.","date_created":"2018-12-11T11:45:03Z","article_processing_charge":"No","external_id":{"isi":["000437018500032"],"arxiv":["1708.01546"]},"title":"Power law decay for systems of randomly coupled differential equations","volume":50,"year":"2018","publication":"SIAM Journal on Mathematical Analysis","project":[{"grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems"},{"call_identifier":"FWF","grant_number":"M02080","name":"Structured Non-Hermitian Random Matrices","_id":"258F40A4-B435-11E9-9278-68D0E5697425"}],"page":"3271 - 3290","publist_id":"7740","type":"journal_article","isi":1,"intvolume":"        50","publisher":"Society for Industrial and Applied Mathematics ","author":[{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"first_name":"Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H"},{"first_name":"David T","orcid":"0000-0003-3493-121X","last_name":"Renfrew","id":"4845BF6A-F248-11E8-B48F-1D18A9856A87","full_name":"Renfrew, David T"}],"_id":"181","quality_controlled":"1","scopus_import":"1","citation":{"chicago":"Erdös, László, Torben H Krüger, and David T Renfrew. “Power Law Decay for Systems of Randomly Coupled Differential Equations.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics , 2018. <a href=\"https://doi.org/10.1137/17M1143125\">https://doi.org/10.1137/17M1143125</a>.","short":"L. Erdös, T.H. Krüger, D.T. Renfrew, SIAM Journal on Mathematical Analysis 50 (2018) 3271–3290.","apa":"Erdös, L., Krüger, T. H., &#38; Renfrew, D. T. (2018). Power law decay for systems of randomly coupled differential equations. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics . <a href=\"https://doi.org/10.1137/17M1143125\">https://doi.org/10.1137/17M1143125</a>","ama":"Erdös L, Krüger TH, Renfrew DT. Power law decay for systems of randomly coupled differential equations. <i>SIAM Journal on Mathematical Analysis</i>. 2018;50(3):3271-3290. doi:<a href=\"https://doi.org/10.1137/17M1143125\">10.1137/17M1143125</a>","mla":"Erdös, László, et al. “Power Law Decay for Systems of Randomly Coupled Differential Equations.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 50, no. 3, Society for Industrial and Applied Mathematics , 2018, pp. 3271–90, doi:<a href=\"https://doi.org/10.1137/17M1143125\">10.1137/17M1143125</a>.","ista":"Erdös L, Krüger TH, Renfrew DT. 2018. Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. 50(3), 3271–3290.","ieee":"L. Erdös, T. H. Krüger, and D. T. Renfrew, “Power law decay for systems of randomly coupled differential equations,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 50, no. 3. Society for Industrial and Applied Mathematics , pp. 3271–3290, 2018."}},{"date_updated":"2025-09-18T07:34:29Z","oa_version":"Published Version","issue":"12","arxiv":1,"oa":1,"ec_funded":1,"language":[{"iso":"eng"}],"day":"13","file":[{"file_size":3084674,"file_name":"2018_Annales_Betea.pdf","file_id":"5866","date_created":"2019-01-21T15:18:55Z","checksum":"0c38abe73569b7166b7487ad5d23cc68","relation":"main_file","content_type":"application/pdf","date_updated":"2020-07-14T12:47:03Z","access_level":"open_access","creator":"dernst"}],"ddc":["500"],"abstract":[{"lang":"eng","text":"We investigate the free boundary Schur process, a variant of the Schur process introduced by Okounkov and Reshetikhin, where we allow the first and the last partitions to be arbitrary (instead of empty in the original setting). The pfaffian Schur process, previously studied by several authors, is recovered when just one of the boundary partitions is left free. We compute the correlation functions of the process in all generality via the free fermion formalism, which we extend with the thorough treatment of “free boundary states.” For the case of one free boundary, our approach yields a new proof that the process is pfaffian. For the case of two free boundaries, we find that the process is not pfaffian, but a closely related process is. We also study three different applications of the Schur process with one free boundary: fluctuations of symmetrized last passage percolation models, limit shapes and processes for symmetric plane partitions and for plane overpartitions."}],"publication_status":"published","date_published":"2018-11-13T00:00:00Z","status":"public","month":"11","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","doi":"10.1007/s00023-018-0723-1","scopus_import":"1","quality_controlled":"1","has_accepted_license":"1","citation":{"ama":"Betea D, Bouttier J, Nejjar P, Vuletic M. The free boundary Schur process and applications I. <i>Annales Henri Poincare</i>. 2018;19(12):3663-3742. doi:<a href=\"https://doi.org/10.1007/s00023-018-0723-1\">10.1007/s00023-018-0723-1</a>","mla":"Betea, Dan, et al. “The Free Boundary Schur Process and Applications I.” <i>Annales Henri Poincare</i>, vol. 19, no. 12, Springer Nature, 2018, pp. 3663–742, doi:<a href=\"https://doi.org/10.1007/s00023-018-0723-1\">10.1007/s00023-018-0723-1</a>.","ista":"Betea D, Bouttier J, Nejjar P, Vuletic M. 2018. The free boundary Schur process and applications I. Annales Henri Poincare. 19(12), 3663–3742.","ieee":"D. Betea, J. Bouttier, P. Nejjar, and M. Vuletic, “The free boundary Schur process and applications I,” <i>Annales Henri Poincare</i>, vol. 19, no. 12. Springer Nature, pp. 3663–3742, 2018.","chicago":"Betea, Dan, Jeremie Bouttier, Peter Nejjar, and Mirjana Vuletic. “The Free Boundary Schur Process and Applications I.” <i>Annales Henri Poincare</i>. Springer Nature, 2018. <a href=\"https://doi.org/10.1007/s00023-018-0723-1\">https://doi.org/10.1007/s00023-018-0723-1</a>.","short":"D. Betea, J. Bouttier, P. Nejjar, M. Vuletic, Annales Henri Poincare 19 (2018) 3663–3742.","apa":"Betea, D., Bouttier, J., Nejjar, P., &#38; Vuletic, M. (2018). The free boundary Schur process and applications I. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-018-0723-1\">https://doi.org/10.1007/s00023-018-0723-1</a>"},"_id":"556","file_date_updated":"2020-07-14T12:47:03Z","author":[{"full_name":"Betea, Dan","first_name":"Dan","last_name":"Betea"},{"full_name":"Bouttier, Jeremie","last_name":"Bouttier","first_name":"Jeremie"},{"full_name":"Nejjar, Peter","last_name":"Nejjar","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","first_name":"Peter"},{"full_name":"Vuletic, Mirjana","last_name":"Vuletic","first_name":"Mirjana"}],"intvolume":"        19","publisher":"Springer Nature","isi":1,"type":"journal_article","publist_id":"7258","page":"3663-3742","volume":19,"title":"The free boundary Schur process and applications I","external_id":{"isi":["000450487900003"],"arxiv":["1704.05809"]},"article_type":"original","publication":"Annales Henri Poincare","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804"},{"grant_number":"716117","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"}],"year":"2018","article_processing_charge":"Yes (via OA deal)","date_created":"2018-12-11T11:47:09Z","publication_identifier":{"issn":["1424-0637"]},"department":[{"_id":"LaEr"},{"_id":"JaMa"}]},{"abstract":[{"lang":"eng","text":"We consider a Wigner-type ensemble, i.e. large hermitian N×N random matrices H=H∗ with centered independent entries and with a general matrix of variances Sxy=𝔼∣∣Hxy∣∣2. The norm of H is asymptotically given by the maximum of the support of the self-consistent density of states. We establish a bound on this maximum in terms of norms of powers of S that substantially improves the earlier bound 2∥S∥1/2∞ given in [O. Ajanki, L. Erdős and T. Krüger, Universality for general Wigner-type matrices, Prob. Theor. Rel. Fields169 (2017) 667–727]. The key element of the proof is an effective Markov chain approximation for the contributions of the weighted Dyck paths appearing in the iterative solution of the corresponding Dyson equation."}],"publication_status":"published","date_published":"2018-09-26T00:00:00Z","status":"public","month":"09","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1802.05175"}],"doi":"10.1142/s2010326319500096","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Preprint","date_updated":"2025-04-15T08:05:02Z","arxiv":1,"oa":1,"language":[{"iso":"eng"}],"ec_funded":1,"day":"26","external_id":{"arxiv":["1802.05175"],"isi":["000477677200002"]},"title":"Bounds on the norm of Wigner-type random matrices","year":"2018","project":[{"grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"publication":"Random matrices: Theory and applications","date_created":"2019-02-13T10:40:54Z","article_processing_charge":"No","publication_identifier":{"issn":["2010-3263"],"eissn":["2010-3271"]},"department":[{"_id":"LaEr"}],"quality_controlled":"1","article_number":"1950009","scopus_import":"1","citation":{"ama":"Erdös L, Mühlbacher P. Bounds on the norm of Wigner-type random matrices. <i>Random matrices: Theory and applications</i>. 2018. doi:<a href=\"https://doi.org/10.1142/s2010326319500096\">10.1142/s2010326319500096</a>","mla":"Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random Matrices.” <i>Random Matrices: Theory and Applications</i>, 1950009, World Scientific Publishing, 2018, doi:<a href=\"https://doi.org/10.1142/s2010326319500096\">10.1142/s2010326319500096</a>.","ista":"Erdös L, Mühlbacher P. 2018. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications., 1950009.","ieee":"L. Erdös and P. Mühlbacher, “Bounds on the norm of Wigner-type random matrices,” <i>Random matrices: Theory and applications</i>. World Scientific Publishing, 2018.","chicago":"Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random Matrices.” <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing, 2018. <a href=\"https://doi.org/10.1142/s2010326319500096\">https://doi.org/10.1142/s2010326319500096</a>.","short":"L. Erdös, P. Mühlbacher, Random Matrices: Theory and Applications (2018).","apa":"Erdös, L., &#38; Mühlbacher, P. (2018). Bounds on the norm of Wigner-type random matrices. <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s2010326319500096\">https://doi.org/10.1142/s2010326319500096</a>"},"author":[{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","full_name":"Erdös, László"},{"last_name":"Mühlbacher","first_name":"Peter","full_name":"Mühlbacher, Peter"}],"_id":"5971","publisher":"World Scientific Publishing","type":"journal_article","isi":1},{"publisher":"Springer","intvolume":"       171","isi":1,"type":"journal_article","citation":{"short":"J. Lee, K. Schnelli, Probability Theory and Related Fields 171 (2018).","apa":"Lee, J., &#38; Schnelli, K. (2018). Local law and Tracy–Widom limit for sparse random matrices. <i>Probability Theory and Related Fields</i>. Springer. <a href=\"https://doi.org/10.1007/s00440-017-0787-8\">https://doi.org/10.1007/s00440-017-0787-8</a>","chicago":"Lee, Jii, and Kevin Schnelli. “Local Law and Tracy–Widom Limit for Sparse Random Matrices.” <i>Probability Theory and Related Fields</i>. Springer, 2018. <a href=\"https://doi.org/10.1007/s00440-017-0787-8\">https://doi.org/10.1007/s00440-017-0787-8</a>.","ieee":"J. Lee and K. Schnelli, “Local law and Tracy–Widom limit for sparse random matrices,” <i>Probability Theory and Related Fields</i>, vol. 171, no. 1–2. Springer, 2018.","ista":"Lee J, Schnelli K. 2018. Local law and Tracy–Widom limit for sparse random matrices. Probability Theory and Related Fields. 171(1–2), 543–616.","mla":"Lee, Jii, and Kevin Schnelli. “Local Law and Tracy–Widom Limit for Sparse Random Matrices.” <i>Probability Theory and Related Fields</i>, vol. 171, no. 1–2, 543–616, Springer, 2018, doi:<a href=\"https://doi.org/10.1007/s00440-017-0787-8\">10.1007/s00440-017-0787-8</a>.","ama":"Lee J, Schnelli K. Local law and Tracy–Widom limit for sparse random matrices. <i>Probability Theory and Related Fields</i>. 2018;171(1-2). doi:<a href=\"https://doi.org/10.1007/s00440-017-0787-8\">10.1007/s00440-017-0787-8</a>"},"article_number":"543-616","quality_controlled":"1","scopus_import":"1","_id":"690","author":[{"last_name":"Lee","first_name":"Jii","full_name":"Lee, Jii"},{"full_name":"Schnelli, Kevin","last_name":"Schnelli","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0954-3231","first_name":"Kevin"}],"article_processing_charge":"No","date_created":"2018-12-11T11:47:56Z","department":[{"_id":"LaEr"}],"publist_id":"7017","publication":"Probability Theory and Related Fields","project":[{"grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"year":"2018","volume":171,"title":"Local law and Tracy–Widom limit for sparse random matrices","external_id":{"arxiv":["1605.08767"],"isi":["000432129600012"]},"day":"14","arxiv":1,"oa_version":"Preprint","date_updated":"2025-09-10T14:00:58Z","issue":"1-2","oa":1,"ec_funded":1,"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1605.08767","open_access":"1"}],"month":"06","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","doi":"10.1007/s00440-017-0787-8","abstract":[{"lang":"eng","text":"We consider spectral properties and the edge universality of sparse random matrices, the class of random matrices that includes the adjacency matrices of the Erdős–Rényi graph model G(N, p). We prove a local law for the eigenvalue density up to the spectral edges. Under a suitable condition on the sparsity, we also prove that the rescaled extremal eigenvalues exhibit GOE Tracy–Widom fluctuations if a deterministic shift of the spectral edge due to the sparsity is included. For the adjacency matrix of the Erdős–Rényi graph this establishes the Tracy–Widom fluctuations of the second largest eigenvalue when p is much larger than N−2/3 with a deterministic shift of order (Np)−1."}],"publication_status":"published","status":"public","date_published":"2018-06-14T00:00:00Z"},{"abstract":[{"text":"We consider the totally asymmetric simple exclusion process in a critical scaling parametrized by a≥0, which creates a shock in the particle density of order aT−1/3, T the observation time. When starting from step initial data, we provide bounds on the limiting law which in particular imply that in the double limit lima→∞limT→∞ one recovers the product limit law and the degeneration of the correlation length observed at shocks of order 1. This result is shown to apply to a general last-passage percolation model. We also obtain bounds on the two-point functions of several airy processes.","lang":"eng"}],"publication_status":"published","ddc":["510"],"status":"public","date_published":"2018-10-01T00:00:00Z","month":"10","doi":"10.30757/ALEA.v15-49","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"issue":"2","date_updated":"2025-04-14T07:27:49Z","oa_version":"Published Version","ec_funded":1,"language":[{"iso":"eng"}],"oa":1,"day":"01","file":[{"file_size":394851,"file_name":"2018_ALEA_Nejjar.pdf","file_id":"5981","date_created":"2019-02-14T09:44:10Z","checksum":"2ded46aa284a836a8cbb34133a64f1cb","relation":"main_file","content_type":"application/pdf","date_updated":"2020-07-14T12:47:46Z","access_level":"open_access","creator":"kschuh"}],"page":"1311-1334","year":"2018","project":[{"name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804"},{"call_identifier":"H2020","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"publication":"Latin American Journal of Probability and Mathematical Statistics","external_id":{"isi":["000460475800022"],"arxiv":["1705.08836"]},"article_type":"original","title":"Transition to shocks in TASEP and decoupling of last passage times","volume":15,"publication_identifier":{"issn":["1980-0436"]},"date_created":"2018-12-11T11:44:28Z","article_processing_charge":"No","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"citation":{"apa":"Nejjar, P. (2018). Transition to shocks in TASEP and decoupling of last passage times. <i>Latin American Journal of Probability and Mathematical Statistics</i>. Instituto Nacional de Matematica Pura e Aplicada. <a href=\"https://doi.org/10.30757/ALEA.v15-49\">https://doi.org/10.30757/ALEA.v15-49</a>","short":"P. Nejjar, Latin American Journal of Probability and Mathematical Statistics 15 (2018) 1311–1334.","chicago":"Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” <i>Latin American Journal of Probability and Mathematical Statistics</i>. Instituto Nacional de Matematica Pura e Aplicada, 2018. <a href=\"https://doi.org/10.30757/ALEA.v15-49\">https://doi.org/10.30757/ALEA.v15-49</a>.","mla":"Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” <i>Latin American Journal of Probability and Mathematical Statistics</i>, vol. 15, no. 2, Instituto Nacional de Matematica Pura e Aplicada, 2018, pp. 1311–34, doi:<a href=\"https://doi.org/10.30757/ALEA.v15-49\">10.30757/ALEA.v15-49</a>.","ista":"Nejjar P. 2018. Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. 15(2), 1311–1334.","ieee":"P. Nejjar, “Transition to shocks in TASEP and decoupling of last passage times,” <i>Latin American Journal of Probability and Mathematical Statistics</i>, vol. 15, no. 2. Instituto Nacional de Matematica Pura e Aplicada, pp. 1311–1334, 2018.","ama":"Nejjar P. Transition to shocks in TASEP and decoupling of last passage times. <i>Latin American Journal of Probability and Mathematical Statistics</i>. 2018;15(2):1311-1334. doi:<a href=\"https://doi.org/10.30757/ALEA.v15-49\">10.30757/ALEA.v15-49</a>"},"has_accepted_license":"1","scopus_import":"1","quality_controlled":"1","author":[{"full_name":"Nejjar, Peter","first_name":"Peter","last_name":"Nejjar","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87"}],"file_date_updated":"2020-07-14T12:47:46Z","_id":"70","publisher":"Instituto Nacional de Matematica Pura e Aplicada","intvolume":"        15","type":"journal_article","isi":1},{"_id":"1012","author":[{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László"},{"first_name":"Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"citation":{"chicago":"Erdös, László, and Dominik J Schröder. “Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2018. <a href=\"https://doi.org/10.1093/imrn/rnw330\">https://doi.org/10.1093/imrn/rnw330</a>.","apa":"Erdös, L., &#38; Schröder, D. J. (2018). Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rnw330\">https://doi.org/10.1093/imrn/rnw330</a>","short":"L. Erdös, D.J. Schröder, International Mathematics Research Notices 2018 (2018) 3255–3298.","ama":"Erdös L, Schröder DJ. Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. <i>International Mathematics Research Notices</i>. 2018;2018(10):3255-3298. doi:<a href=\"https://doi.org/10.1093/imrn/rnw330\">10.1093/imrn/rnw330</a>","ista":"Erdös L, Schröder DJ. 2018. Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. 2018(10), 3255–3298.","mla":"Erdös, László, and Dominik J. Schröder. “Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues.” <i>International Mathematics Research Notices</i>, vol. 2018, no. 10, Oxford University Press, 2018, pp. 3255–98, doi:<a href=\"https://doi.org/10.1093/imrn/rnw330\">10.1093/imrn/rnw330</a>.","ieee":"L. Erdös and D. J. Schröder, “Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues,” <i>International Mathematics Research Notices</i>, vol. 2018, no. 10. Oxford University Press, pp. 3255–3298, 2018."},"quality_controlled":"1","scopus_import":"1","isi":1,"type":"journal_article","publisher":"Oxford University Press","intvolume":"      2018","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804"}],"publication":"International Mathematics Research Notices","year":"2018","volume":2018,"external_id":{"isi":["000441668300009"],"arxiv":["1608.05163"]},"title":"Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues","related_material":{"record":[{"id":"6179","status":"public","relation":"dissertation_contains"}]},"publist_id":"6383","page":"3255-3298","department":[{"_id":"LaEr"}],"publication_identifier":{"issn":["1073-7928"]},"article_processing_charge":"No","date_created":"2018-12-11T11:49:41Z","ec_funded":1,"language":[{"iso":"eng"}],"oa":1,"arxiv":1,"date_updated":"2026-04-08T13:55:03Z","oa_version":"Preprint","issue":"10","day":"18","status":"public","date_published":"2018-05-18T00:00:00Z","abstract":[{"text":"We prove a new central limit theorem (CLT) for the difference of linear eigenvalue statistics of a Wigner random matrix H and its minor H and find that the fluctuation is much smaller than the fluctuations of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of H and H. In particular, our theorem identifies the fluctuation of Kerov's rectangular Young diagrams, defined by the interlacing eigenvalues ofH and H, around their asymptotic shape, the Vershik'Kerov'Logan'Shepp curve. Young diagrams equipped with the Plancherel measure follow the same limiting shape. For this, algebraically motivated, ensemble a CLT has been obtained in Ivanov and Olshanski [20] which is structurally similar to our result but the variance is different, indicating that the analogy between the two models has its limitations. Moreover, our theorem shows that Borodin's result [7] on the convergence of the spectral distribution of Wigner matrices to a Gaussian free field also holds in derivative sense.","lang":"eng"}],"publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1093/imrn/rnw330","main_file_link":[{"url":"https://arxiv.org/abs/1608.05163","open_access":"1"}],"month":"05"},{"day":"12","file":[{"content_type":"application/pdf","relation":"main_file","creator":"dernst","access_level":"open_access","date_updated":"2020-07-14T12:44:57Z","file_size":5801709,"file_name":"2018_thesis_Alt.pdf","checksum":"d4dad55a7513f345706aaaba90cb1bb8","date_created":"2019-04-08T13:55:20Z","file_id":"6241"},{"content_type":"application/zip","relation":"source_file","creator":"dernst","access_level":"closed","date_updated":"2020-07-14T12:44:57Z","file_size":3802059,"file_name":"2018_thesis_Alt_source.zip","checksum":"d73fcf46300dce74c403f2b491148ab4","date_created":"2019-04-08T13:55:20Z","file_id":"6242"}],"corr_author":"1","oa_version":"Published Version","date_updated":"2026-04-08T14:11:37Z","alternative_title":["ISTA Thesis"],"language":[{"iso":"eng"}],"oa":1,"ec_funded":1,"month":"07","tmp":{"short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","supervisor":[{"first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László"}],"doi":"10.15479/AT:ISTA:TH_1040","ddc":["515","519"],"abstract":[{"lang":"eng","text":"The eigenvalue density of many large random matrices is well approximated by a deterministic measure, the self-consistent density of states. In the present work, we show this behaviour for several classes of random matrices. In fact, we establish that, in each of these classes, the self-consistent density of states approximates the eigenvalue density of the random matrix on all scales slightly above the typical eigenvalue spacing. For large classes of random matrices, the self-consistent density of states exhibits several universal features. We prove that, under suitable assumptions, random Gram matrices and Hermitian random matrices with decaying correlations have a 1/3-Hölder continuous self-consistent density of states ρ on R, which is analytic, where it is positive, and has either a square root edge or a cubic root cusp, where it vanishes. We, thus, extend the validity of the corresponding result for Wigner-type matrices from [4, 5, 7]. We show that ρ is determined as the inverse Stieltjes transform of the normalized trace of the unique solution m(z) to the Dyson equation −m(z) −1 = z − a + S[m(z)] on C N×N with the constraint Im m(z) ≥ 0. Here, z lies in the complex upper half-plane, a is a self-adjoint element of C N×N and S is a positivity-preserving operator on C N×N encoding the first two moments of the random matrix. In order to analyze a possible limit of ρ for N → ∞ and address some applications in free probability theory, we also consider the Dyson equation on infinite dimensional von Neumann algebras. We present two applications to random matrices. We first establish that, under certain assumptions, large random matrices with independent entries have a rotationally symmetric self-consistent density of states which is supported on a centered disk in C. Moreover, it is infinitely often differentiable apart from a jump on the boundary of this disk. Second, we show edge universality at all regular (not necessarily extreme) spectral edges for Hermitian random matrices with decaying correlations."}],"publication_status":"published","status":"public","date_published":"2018-07-12T00:00:00Z","publisher":"Institute of Science and Technology Austria","type":"dissertation","citation":{"ieee":"J. Alt, “Dyson equation and eigenvalue statistics of random matrices,” Institute of Science and Technology Austria, 2018.","mla":"Alt, Johannes. <i>Dyson Equation and Eigenvalue Statistics of Random Matrices</i>. Institute of Science and Technology Austria, 2018, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:TH_1040\">10.15479/AT:ISTA:TH_1040</a>.","ista":"Alt J. 2018. Dyson equation and eigenvalue statistics of random matrices. Institute of Science and Technology Austria.","ama":"Alt J. Dyson equation and eigenvalue statistics of random matrices. 2018. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:TH_1040\">10.15479/AT:ISTA:TH_1040</a>","apa":"Alt, J. (2018). <i>Dyson equation and eigenvalue statistics of random matrices</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:TH_1040\">https://doi.org/10.15479/AT:ISTA:TH_1040</a>","short":"J. Alt, Dyson Equation and Eigenvalue Statistics of Random Matrices, Institute of Science and Technology Austria, 2018.","chicago":"Alt, Johannes. “Dyson Equation and Eigenvalue Statistics of Random Matrices.” Institute of Science and Technology Austria, 2018. <a href=\"https://doi.org/10.15479/AT:ISTA:TH_1040\">https://doi.org/10.15479/AT:ISTA:TH_1040</a>."},"has_accepted_license":"1","file_date_updated":"2020-07-14T12:44:57Z","_id":"149","author":[{"full_name":"Alt, Johannes","last_name":"Alt","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","first_name":"Johannes"}],"publication_identifier":{"issn":["2663-337X"]},"article_processing_charge":"No","date_created":"2018-12-11T11:44:53Z","department":[{"_id":"LaEr"}],"related_material":{"record":[{"status":"public","id":"6240","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"6184","status":"public"},{"status":"public","id":"566","relation":"part_of_dissertation"},{"status":"public","id":"6183","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"1010","status":"public"},{"relation":"part_of_dissertation","id":"550","status":"public"},{"id":"1677","status":"public","relation":"part_of_dissertation"}]},"publist_id":"7772","degree_awarded":"PhD","pubrep_id":"1040","OA_place":"publisher","page":"456","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7"}],"year":"2018","title":"Dyson equation and eigenvalue statistics of random matrices"},{"isi":1,"type":"journal_article","publisher":"Institute of Mathematical Statistics","intvolume":"        28","_id":"566","author":[{"full_name":"Alt, Johannes","first_name":"Johannes","last_name":"Alt","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László"},{"orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","last_name":"Krüger","first_name":"Torben H","full_name":"Krüger, Torben H"}],"citation":{"chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “Local Inhomogeneous Circular Law.” <i>Annals Applied Probability </i>. Institute of Mathematical Statistics, 2018. <a href=\"https://doi.org/10.1214/17-AAP1302\">https://doi.org/10.1214/17-AAP1302</a>.","apa":"Alt, J., Erdös, L., &#38; Krüger, T. H. (2018). Local inhomogeneous circular law. <i>Annals Applied Probability </i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/17-AAP1302\">https://doi.org/10.1214/17-AAP1302</a>","short":"J. Alt, L. Erdös, T.H. Krüger, Annals Applied Probability  28 (2018) 148–203.","ama":"Alt J, Erdös L, Krüger TH. Local inhomogeneous circular law. <i>Annals Applied Probability </i>. 2018;28(1):148-203. doi:<a href=\"https://doi.org/10.1214/17-AAP1302\">10.1214/17-AAP1302</a>","mla":"Alt, Johannes, et al. “Local Inhomogeneous Circular Law.” <i>Annals Applied Probability </i>, vol. 28, no. 1, Institute of Mathematical Statistics, 2018, pp. 148–203, doi:<a href=\"https://doi.org/10.1214/17-AAP1302\">10.1214/17-AAP1302</a>.","ista":"Alt J, Erdös L, Krüger TH. 2018. Local inhomogeneous circular law. Annals Applied Probability . 28(1), 148–203.","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “Local inhomogeneous circular law,” <i>Annals Applied Probability </i>, vol. 28, no. 1. Institute of Mathematical Statistics, pp. 148–203, 2018."},"scopus_import":"1","quality_controlled":"1","department":[{"_id":"LaEr"}],"article_processing_charge":"No","date_created":"2018-12-11T11:47:13Z","project":[{"grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"publication":"Annals Applied Probability ","year":"2018","volume":28,"title":"Local inhomogeneous circular law","external_id":{"isi":["000431721800005"],"arxiv":["1612.07776 "]},"article_type":"original","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"149"}]},"page":"148-203","corr_author":"1","day":"03","language":[{"iso":"eng"}],"oa":1,"ec_funded":1,"arxiv":1,"date_updated":"2026-04-08T14:11:36Z","oa_version":"Preprint","issue":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","doi":"10.1214/17-AAP1302","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1612.07776 "}],"month":"03","status":"public","date_published":"2018-03-03T00:00:00Z","publication_status":"published","abstract":[{"lang":"eng","text":"We consider large random matrices X with centered, independent entries which have comparable but not necessarily identical variances. Girko's circular law asserts that the spectrum is supported in a disk and in case of identical variances, the limiting density is uniform. In this special case, the local circular law by Bourgade et. al. [11,12] shows that the empirical density converges even locally on scales slightly above the typical eigenvalue spacing. In the general case, the limiting density is typically inhomogeneous and it is obtained via solving a system of deterministic equations. Our main result is the local inhomogeneous circular law in the bulk spectrum on the optimal scale for a general variance profile of the entries of X. \r\n\r\n"}]}]