[{"department":[{"_id":"LaEr"}],"publisher":"Formal Power Series and Algebraic Combinatorics","publication_status":"published","year":"2019","acknowledgement":"D.B. is especially grateful to Patrik Ferrari for suggesting simplifications in Section 3 and\r\nto Alessandra Occelli for suggesting the name for the models of Section 2.\r\n","date_updated":"2021-01-12T08:17:18Z","date_created":"2020-07-26T22:01:04Z","author":[{"first_name":"Dan","last_name":"Betea","full_name":"Betea, Dan"},{"last_name":"Bouttier","first_name":"Jérémie","full_name":"Bouttier, Jérémie"},{"full_name":"Nejjar, Peter","first_name":"Peter","last_name":"Nejjar","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Vuletíc, Mirjana","first_name":"Mirjana","last_name":"Vuletíc"}],"article_number":"34","ec_funded":1,"project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1902.08750"}],"external_id":{"arxiv":["1902.08750"]},"oa":1,"language":[{"iso":"eng"}],"conference":{"name":"FPSAC: International Conference on Formal Power Series and Algebraic Combinatorics","end_date":"2019-07-05","location":"Ljubljana, Slovenia","start_date":"2019-07-01"},"month":"07","status":"public","title":"New edge asymptotics of skew Young diagrams via free boundaries","_id":"8175","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","type":"conference","abstract":[{"text":"We study edge asymptotics of poissonized Plancherel-type measures on skew Young diagrams (integer partitions). These measures can be seen as generalizations of those studied by Baik--Deift--Johansson and Baik--Rains in resolving Ulam's problem on longest increasing subsequences of random permutations and the last passage percolation (corner growth) discrete versions thereof. Moreover they interpolate between said measures and the uniform measure on partitions. In the new KPZ-like 1/3 exponent edge scaling limit with logarithmic corrections, we find new probability distributions generalizing the classical Tracy--Widom GUE, GOE and GSE distributions from the theory of random matrices.","lang":"eng"}],"citation":{"mla":"Betea, Dan, et al. “New Edge Asymptotics of Skew Young Diagrams via Free Boundaries.” Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics, 34, Formal Power Series and Algebraic Combinatorics, 2019.","short":"D. Betea, J. Bouttier, P. Nejjar, M. Vuletíc, in:, Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics, Formal Power Series and Algebraic Combinatorics, 2019.","chicago":"Betea, Dan, Jérémie Bouttier, Peter Nejjar, and Mirjana Vuletíc. “New Edge Asymptotics of Skew Young Diagrams via Free Boundaries.” In Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. Formal Power Series and Algebraic Combinatorics, 2019.","ama":"Betea D, Bouttier J, Nejjar P, Vuletíc M. New edge asymptotics of skew Young diagrams via free boundaries. In: Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. Formal Power Series and Algebraic Combinatorics; 2019.","ista":"Betea D, Bouttier J, Nejjar P, Vuletíc M. 2019. New edge asymptotics of skew Young diagrams via free boundaries. Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. FPSAC: International Conference on Formal Power Series and Algebraic Combinatorics, 34.","ieee":"D. Betea, J. Bouttier, P. Nejjar, and M. Vuletíc, “New edge asymptotics of skew Young diagrams via free boundaries,” in Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics, Ljubljana, Slovenia, 2019.","apa":"Betea, D., Bouttier, J., Nejjar, P., & Vuletíc, M. (2019). New edge asymptotics of skew Young diagrams via free boundaries. In Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. Ljubljana, Slovenia: Formal Power Series and Algebraic Combinatorics."},"publication":"Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics","date_published":"2019-07-01T00:00:00Z","scopus_import":"1","article_processing_charge":"No","day":"01"},{"publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Elsevier","year":"2019","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)","date_created":"2018-12-11T11:46:17Z","date_updated":"2023-08-24T14:31:47Z","volume":576,"author":[{"full_name":"Virosztek, Daniel","orcid":"0000-0003-1109-5511","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","last_name":"Virosztek","first_name":"Daniel"}],"ec_funded":1,"publist_id":"7424","quality_controlled":"1","isi":1,"project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"main_file_link":[{"url":"https://arxiv.org/abs/1712.05324","open_access":"1"}],"external_id":{"isi":["000470955300005"],"arxiv":["1712.05324"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1016/j.laa.2018.03.002","month":"09","status":"public","title":"Jointly convex quantum Jensen divergences","intvolume":" 576","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"405","oa_version":"Preprint","type":"journal_article","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."}],"article_type":"original","page":"67-78","publication":"Linear Algebra and Its Applications","citation":{"ama":"Virosztek D. Jointly convex quantum Jensen divergences. Linear Algebra and Its Applications. 2019;576:67-78. doi:10.1016/j.laa.2018.03.002","apa":"Virosztek, D. (2019). Jointly convex quantum Jensen divergences. Linear Algebra and Its Applications. Elsevier. https://doi.org/10.1016/j.laa.2018.03.002","ieee":"D. Virosztek, “Jointly convex quantum Jensen divergences,” Linear Algebra and Its Applications, vol. 576. Elsevier, pp. 67–78, 2019.","ista":"Virosztek D. 2019. Jointly convex quantum Jensen divergences. Linear Algebra and Its Applications. 576, 67–78.","short":"D. Virosztek, Linear Algebra and Its Applications 576 (2019) 67–78.","mla":"Virosztek, Daniel. “Jointly Convex Quantum Jensen Divergences.” Linear Algebra and Its Applications, vol. 576, Elsevier, 2019, pp. 67–78, doi:10.1016/j.laa.2018.03.002.","chicago":"Virosztek, Daniel. “Jointly Convex Quantum Jensen Divergences.” Linear Algebra and Its Applications. Elsevier, 2019. https://doi.org/10.1016/j.laa.2018.03.002."},"date_published":"2019-09-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No"},{"year":"2019","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).\r\n","publisher":"Springer","department":[{"_id":"LaEr"}],"publication_status":"published","author":[{"id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87","last_name":"Ajanki","first_name":"Oskari H","full_name":"Ajanki, Oskari H"},{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"Krüger, Torben H","last_name":"Krüger","first_name":"Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87"}],"volume":173,"date_updated":"2023-08-24T14:39:00Z","date_created":"2018-12-11T11:46:25Z","publist_id":"7394","ec_funded":1,"file_date_updated":"2020-07-14T12:46:26Z","license":"https://creativecommons.org/licenses/by/4.0/","external_id":{"isi":["000459396500007"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"isi":1,"quality_controlled":"1","doi":"10.1007/s00440-018-0835-z","language":[{"iso":"eng"}],"publication_identifier":{"issn":["01788051"],"eissn":["14322064"]},"month":"02","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"429","intvolume":" 173","title":"Stability of the matrix Dyson equation and random matrices with correlations","status":"public","ddc":["510"],"file":[{"checksum":"f9354fa5c71f9edd17132588f0dc7d01","date_updated":"2020-07-14T12:46:26Z","date_created":"2018-12-17T16:12:08Z","file_id":"5720","relation":"main_file","creator":"dernst","file_size":1201840,"content_type":"application/pdf","access_level":"open_access","file_name":"2018_ProbTheory_Ajanki.pdf"}],"oa_version":"Published Version","type":"journal_article","issue":"1-2","abstract":[{"lang":"eng","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."}],"citation":{"ama":"Ajanki OH, Erdös L, Krüger TH. Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. 2019;173(1-2):293–373. doi:10.1007/s00440-018-0835-z","apa":"Ajanki, O. H., Erdös, L., & Krüger, T. H. (2019). Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-018-0835-z","ieee":"O. H. Ajanki, L. Erdös, and T. H. Krüger, “Stability of the matrix Dyson equation and random matrices with correlations,” Probability Theory and Related Fields, vol. 173, no. 1–2. Springer, pp. 293–373, 2019.","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.","short":"O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields 173 (2019) 293–373.","mla":"Ajanki, Oskari H., et al. “Stability of the Matrix Dyson Equation and Random Matrices with Correlations.” Probability Theory and Related Fields, vol. 173, no. 1–2, Springer, 2019, pp. 293–373, doi:10.1007/s00440-018-0835-z.","chicago":"Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Stability of the Matrix Dyson Equation and Random Matrices with Correlations.” Probability Theory and Related Fields. Springer, 2019. https://doi.org/10.1007/s00440-018-0835-z."},"publication":"Probability Theory and Related Fields","page":"293–373","article_type":"original","date_published":"2019-02-01T00:00:00Z","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01"},{"status":"public","title":"Singular analytic linear cocycles with negative infinite Lyapunov exponents","intvolume":" 39","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6086","oa_version":"Preprint","type":"journal_article","abstract":[{"lang":"eng","text":"We show that linear analytic cocycles where all Lyapunov exponents are negative infinite are nilpotent. For such one-frequency cocycles we show that they can be analytically conjugated to an upper triangular cocycle or a Jordan normal form. As a consequence, an arbitrarily small analytic perturbation leads to distinct Lyapunov exponents. Moreover, in the one-frequency case where the th Lyapunov exponent is finite and the st negative infinite, we obtain a simple criterion for domination in which case there is a splitting into a nilpotent part and an invertible part."}],"issue":"4","page":"1082-1098","publication":"Ergodic Theory and Dynamical Systems","citation":{"chicago":"Sadel, Christian, and Disheng Xu. “Singular Analytic Linear Cocycles with Negative Infinite Lyapunov Exponents.” Ergodic Theory and Dynamical Systems. Cambridge University Press, 2019. https://doi.org/10.1017/etds.2017.52.","mla":"Sadel, Christian, and Disheng Xu. “Singular Analytic Linear Cocycles with Negative Infinite Lyapunov Exponents.” Ergodic Theory and Dynamical Systems, vol. 39, no. 4, Cambridge University Press, 2019, pp. 1082–98, doi:10.1017/etds.2017.52.","short":"C. Sadel, D. Xu, Ergodic Theory and Dynamical Systems 39 (2019) 1082–1098.","ista":"Sadel C, Xu D. 2019. Singular analytic linear cocycles with negative infinite Lyapunov exponents. Ergodic Theory and Dynamical Systems. 39(4), 1082–1098.","apa":"Sadel, C., & Xu, D. (2019). Singular analytic linear cocycles with negative infinite Lyapunov exponents. Ergodic Theory and Dynamical Systems. Cambridge University Press. https://doi.org/10.1017/etds.2017.52","ieee":"C. Sadel and D. Xu, “Singular analytic linear cocycles with negative infinite Lyapunov exponents,” Ergodic Theory and Dynamical Systems, vol. 39, no. 4. Cambridge University Press, pp. 1082–1098, 2019.","ama":"Sadel C, Xu D. Singular analytic linear cocycles with negative infinite Lyapunov exponents. Ergodic Theory and Dynamical Systems. 2019;39(4):1082-1098. doi:10.1017/etds.2017.52"},"date_published":"2019-04-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No","publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Cambridge University Press","year":"2019","date_updated":"2023-08-25T08:03:30Z","date_created":"2019-03-10T22:59:18Z","volume":39,"author":[{"orcid":"0000-0001-8255-3968","id":"4760E9F8-F248-11E8-B48F-1D18A9856A87","last_name":"Sadel","first_name":"Christian","full_name":"Sadel, Christian"},{"full_name":"Xu, Disheng","first_name":"Disheng","last_name":"Xu"}],"ec_funded":1,"quality_controlled":"1","isi":1,"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"external_id":{"arxiv":["1601.06118"],"isi":["000459725600012"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1601.06118"}],"language":[{"iso":"eng"}],"doi":"10.1017/etds.2017.52","month":"04"},{"scopus_import":"1","day":"01","article_processing_charge":"No","page":"1270-1334","publication":"Annals of Probability","citation":{"ista":"Bao Z, Erdös L, Schnelli K. 2019. Local single ring theorem on optimal scale. Annals of Probability. 47(3), 1270–1334.","apa":"Bao, Z., Erdös, L., & Schnelli, K. (2019). Local single ring theorem on optimal scale. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/18-AOP1284","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Local single ring theorem on optimal scale,” Annals of Probability, vol. 47, no. 3. Institute of Mathematical Statistics, pp. 1270–1334, 2019.","ama":"Bao Z, Erdös L, Schnelli K. Local single ring theorem on optimal scale. Annals of Probability. 2019;47(3):1270-1334. doi:10.1214/18-AOP1284","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Single Ring Theorem on Optimal Scale.” Annals of Probability. Institute of Mathematical Statistics, 2019. https://doi.org/10.1214/18-AOP1284.","mla":"Bao, Zhigang, et al. “Local Single Ring Theorem on Optimal Scale.” Annals of Probability, vol. 47, no. 3, Institute of Mathematical Statistics, 2019, pp. 1270–334, doi:10.1214/18-AOP1284.","short":"Z. Bao, L. Erdös, K. Schnelli, Annals of Probability 47 (2019) 1270–1334."},"date_published":"2019-05-01T00:00:00Z","type":"journal_article","abstract":[{"lang":"eng","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)."}],"issue":"3","status":"public","title":"Local single ring theorem on optimal scale","intvolume":" 47","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6511","oa_version":"Preprint","month":"05","publication_identifier":{"issn":["00911798"]},"isi":1,"quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"external_id":{"arxiv":["1612.05920"],"isi":["000466616100003"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1612.05920","open_access":"1"}],"language":[{"iso":"eng"}],"doi":"10.1214/18-AOP1284","ec_funded":1,"publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","year":"2019","date_updated":"2023-08-28T09:32:29Z","date_created":"2019-06-02T21:59:13Z","volume":47,"author":[{"full_name":"Bao, Zhigang","last_name":"Bao","first_name":"Zhigang","orcid":"0000-0003-3036-1475","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"last_name":"Schnelli","first_name":"Kevin","orcid":"0000-0003-0954-3231","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","full_name":"Schnelli, Kevin"}]},{"type":"journal_article","issue":"2","abstract":[{"lang":"eng","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
Journal of Mathematical Analysis and Applications, vol. 480, no. 2, 123435, Elsevier, 2019, doi:10.1016/j.jmaa.2019.123435.","chicago":"Gehér, György Pál, Tamás Titkos, and Daniel Virosztek. “On Isometric Embeddings of Wasserstein Spaces – the Discrete Case.” Journal of Mathematical Analysis and Applications. Elsevier, 2019. https://doi.org/10.1016/j.jmaa.2019.123435.","ama":"Gehér GP, Titkos T, Virosztek D. On isometric embeddings of Wasserstein spaces – the discrete case. Journal of Mathematical Analysis and Applications. 2019;480(2). doi:10.1016/j.jmaa.2019.123435","ieee":"G. P. Gehér, T. Titkos, and D. Virosztek, “On isometric embeddings of Wasserstein spaces – the discrete case,” Journal of Mathematical Analysis and Applications, vol. 480, no. 2. Elsevier, 2019.","apa":"Gehér, G. P., Titkos, T., & Virosztek, D. (2019). On isometric embeddings of Wasserstein spaces – the discrete case. Journal of Mathematical Analysis and Applications. Elsevier. https://doi.org/10.1016/j.jmaa.2019.123435","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."},"publication":"Journal of Mathematical Analysis and Applications","date_published":"2019-12-15T00:00:00Z","article_number":"123435","ec_funded":1,"department":[{"_id":"LaEr"}],"publisher":"Elsevier","publication_status":"published","year":"2019","volume":480,"date_updated":"2023-08-29T07:18:50Z","date_created":"2019-09-01T22:01:01Z","author":[{"full_name":"Gehér, György Pál","first_name":"György Pál","last_name":"Gehér"},{"first_name":"Tamás","last_name":"Titkos","full_name":"Titkos, Tamás"},{"id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-1109-5511","first_name":"Daniel","last_name":"Virosztek","full_name":"Virosztek, Daniel"}],"publication_identifier":{"issn":["0022247X"],"eissn":["10960813"]},"month":"12","project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"quality_controlled":"1","isi":1,"main_file_link":[{"url":"https://arxiv.org/abs/1809.01101","open_access":"1"}],"oa":1,"external_id":{"arxiv":["1809.01101"],"isi":["000486563900031"]},"language":[{"iso":"eng"}],"doi":"10.1016/j.jmaa.2019.123435"},{"publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"publication_status":"published","year":"2019","volume":55,"date_created":"2020-01-30T10:36:50Z","date_updated":"2023-09-06T14:58:39Z","author":[{"last_name":"Akemann","first_name":"Gernot","full_name":"Akemann, Gernot"},{"first_name":"Tomasz","last_name":"Checinski","full_name":"Checinski, Tomasz"},{"full_name":"Liu, Dangzheng","first_name":"Dangzheng","last_name":"Liu","id":"2F947E34-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Strahov","first_name":"Eugene","full_name":"Strahov, Eugene"}],"publication_identifier":{"issn":["0246-0203"]},"month":"02","isi":1,"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1704.05224"}],"oa":1,"external_id":{"arxiv":["1704.05224"],"isi":["000456070200013"]},"language":[{"iso":"eng"}],"doi":"10.1214/18-aihp888","type":"journal_article","issue":"1","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."}],"intvolume":" 55","status":"public","title":"Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles","_id":"7423","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Preprint","article_processing_charge":"No","day":"01","page":"441-479","article_type":"original","citation":{"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. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. 2019;55(1):441-479. doi:10.1214/18-aihp888","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,” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, vol. 55, no. 1. Institute of Mathematical Statistics, pp. 441–479, 2019.","apa":"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. Institute of Mathematical Statistics. https://doi.org/10.1214/18-aihp888","mla":"Akemann, Gernot, et al. “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, vol. 55, no. 1, Institute of Mathematical Statistics, 2019, pp. 441–79, doi:10.1214/18-aihp888.","short":"G. Akemann, T. Checinski, D. Liu, E. Strahov, Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55 (2019) 441–479.","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.” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. Institute of Mathematical Statistics, 2019. https://doi.org/10.1214/18-aihp888."},"publication":"Annales de l'Institut Henri Poincaré, Probabilités et Statistiques","date_published":"2019-02-01T00:00:00Z"},{"ddc":["510"],"status":"public","title":"Random matrices with slow correlation decay","intvolume":" 7","_id":"6182","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Published Version","file":[{"content_type":"application/pdf","file_size":1520344,"creator":"dernst","access_level":"open_access","file_name":"2019_Forum_Erdoes.pdf","checksum":"933a472568221c73b2c3ce8c87bf6d15","date_updated":"2020-07-14T12:47:22Z","date_created":"2019-09-17T14:24:13Z","relation":"main_file","file_id":"6883"}],"type":"journal_article","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"}],"article_type":"original","publication":"Forum of Mathematics, Sigma","citation":{"mla":"Erdös, László, et al. “Random Matrices with Slow Correlation Decay.” Forum of Mathematics, Sigma, vol. 7, e8, Cambridge University Press, 2019, doi:10.1017/fms.2019.2.","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Forum of Mathematics, Sigma 7 (2019).","chicago":"Erdös, László, Torben H Krüger, and Dominik J Schröder. “Random Matrices with Slow Correlation Decay.” Forum of Mathematics, Sigma. Cambridge University Press, 2019. https://doi.org/10.1017/fms.2019.2.","ama":"Erdös L, Krüger TH, Schröder DJ. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 2019;7. doi:10.1017/fms.2019.2","ista":"Erdös L, Krüger TH, Schröder DJ. 2019. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 7, e8.","apa":"Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Random matrices with slow correlation decay. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2019.2","ieee":"L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation decay,” Forum of Mathematics, Sigma, vol. 7. Cambridge University Press, 2019."},"date_published":"2019-03-26T00:00:00Z","scopus_import":"1","day":"26","has_accepted_license":"1","article_processing_charge":"No","publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Cambridge University Press","year":"2019","date_created":"2019-03-28T09:05:23Z","date_updated":"2023-09-07T12:54:12Z","volume":7,"author":[{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","last_name":"Krüger","first_name":"Torben H"},{"full_name":"Schröder, Dominik J","last_name":"Schröder","first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"related_material":{"record":[{"id":"6179","relation":"dissertation_contains","status":"public"}]},"article_number":"e8","file_date_updated":"2020-07-14T12:47:22Z","ec_funded":1,"isi":1,"quality_controlled":"1","project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["1705.10661"],"isi":["000488847100001"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1017/fms.2019.2","month":"03","publication_identifier":{"eissn":["20505094"]}},{"citation":{"chicago":"Cipolloni, Giorgio, László Erdös, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” Pure and Applied Analysis . MSP, 2019. https://doi.org/10.2140/paa.2019.1.615.","mla":"Cipolloni, Giorgio, et al. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” Pure and Applied Analysis , vol. 1, no. 4, MSP, 2019, pp. 615–707, doi:10.2140/paa.2019.1.615.","short":"G. Cipolloni, L. Erdös, T.H. Krüger, D.J. Schröder, Pure and Applied Analysis 1 (2019) 615–707.","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.","ieee":"G. Cipolloni, L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices, II: The real symmetric case,” Pure and Applied Analysis , vol. 1, no. 4. MSP, pp. 615–707, 2019.","apa":"Cipolloni, G., Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . MSP. https://doi.org/10.2140/paa.2019.1.615","ama":"Cipolloni G, Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . 2019;1(4):615–707. doi:10.2140/paa.2019.1.615"},"publication":"Pure and Applied Analysis ","page":"615–707","article_type":"original","date_published":"2019-10-12T00:00:00Z","article_processing_charge":"No","day":"12","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"6186","intvolume":" 1","status":"public","title":"Cusp universality for random matrices, II: The real symmetric case","oa_version":"Preprint","type":"journal_article","issue":"4","abstract":[{"lang":"eng","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."}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1811.04055","open_access":"1"}],"external_id":{"arxiv":["1811.04055"]},"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","call_identifier":"H2020","name":"International IST Doctoral Program"}],"quality_controlled":"1","doi":"10.2140/paa.2019.1.615","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["2578-5885"],"issn":["2578-5893"]},"month":"10","year":"2019","publisher":"MSP","department":[{"_id":"LaEr"}],"publication_status":"published","related_material":{"record":[{"id":"6179","status":"public","relation":"dissertation_contains"}]},"author":[{"last_name":"Cipolloni","first_name":"Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","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":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","first_name":"Dominik J","last_name":"Schröder"}],"volume":1,"date_updated":"2023-09-07T12:54:12Z","date_created":"2019-03-28T10:21:17Z","ec_funded":1},{"type":"journal_article","abstract":[{"text":"We study effects of a bounded and compactly supported perturbation on multidimensional continuum random Schrödinger operators in the region of complete localisation. Our main emphasis is on Anderson orthogonality for random Schrödinger operators. Among others, we prove that Anderson orthogonality does occur for Fermi energies in the region of complete localisation with a non-zero probability. This partially confirms recent non-rigorous findings [V. Khemani et al., Nature Phys. 11 (2015), 560–565]. The spectral shift function plays an important role in our analysis of Anderson orthogonality. We identify it with the index of the corresponding pair of spectral projections and explore the consequences thereof. All our results rely on the main technical estimate of this paper which guarantees separate exponential decay of the disorder-averaged Schatten p-norm of χa(f(H)−f(Hτ))χb in a and b. Here, Hτ is a perturbation of the random Schrödinger operator H, χa is the multiplication operator corresponding to the indicator function of a unit cube centred about a∈Rd, and f is in a suitable class of functions of bounded variation with distributional derivative supported in the region of complete localisation for H.","lang":"eng"}],"issue":"3","_id":"10879","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","title":"Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function","status":"public","intvolume":" 9","oa_version":"Preprint","scopus_import":"1","keyword":["Random Schrödinger operators","spectral shift function","Anderson orthogonality"],"day":"01","article_processing_charge":"No","publication":"Journal of Spectral Theory","citation":{"chicago":"Dietlein, Adrian M, Martin Gebert, and Peter Müller. “Perturbations of Continuum Random Schrödinger Operators with Applications to Anderson Orthogonality and the Spectral Shift Function.” Journal of Spectral Theory. European Mathematical Society Publishing House, 2019. https://doi.org/10.4171/jst/267.","mla":"Dietlein, Adrian M., et al. “Perturbations of Continuum Random Schrödinger Operators with Applications to Anderson Orthogonality and the Spectral Shift Function.” Journal of Spectral Theory, vol. 9, no. 3, European Mathematical Society Publishing House, 2019, pp. 921–65, doi:10.4171/jst/267.","short":"A.M. Dietlein, M. Gebert, P. Müller, Journal of Spectral Theory 9 (2019) 921–965.","ista":"Dietlein AM, Gebert M, Müller P. 2019. Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function. Journal of Spectral Theory. 9(3), 921–965.","apa":"Dietlein, A. M., Gebert, M., & Müller, P. (2019). Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function. Journal of Spectral Theory. European Mathematical Society Publishing House. https://doi.org/10.4171/jst/267","ieee":"A. M. Dietlein, M. Gebert, and P. Müller, “Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function,” Journal of Spectral Theory, vol. 9, no. 3. European Mathematical Society Publishing House, pp. 921–965, 2019.","ama":"Dietlein AM, Gebert M, Müller P. Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function. Journal of Spectral Theory. 2019;9(3):921-965. doi:10.4171/jst/267"},"article_type":"original","page":"921-965","date_published":"2019-03-01T00:00:00Z","acknowledgement":"M.G. was supported by the DFG under grant GE 2871/1-1.","year":"2019","publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"European Mathematical Society Publishing House","author":[{"full_name":"Dietlein, Adrian M","id":"317CB464-F248-11E8-B48F-1D18A9856A87","first_name":"Adrian M","last_name":"Dietlein"},{"last_name":"Gebert","first_name":"Martin","full_name":"Gebert, Martin"},{"full_name":"Müller, Peter","last_name":"Müller","first_name":"Peter"}],"date_updated":"2023-09-08T11:35:31Z","date_created":"2022-03-18T12:36:42Z","volume":9,"month":"03","publication_identifier":{"issn":["1664-039X"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1701.02956","open_access":"1"}],"external_id":{"isi":["000484709400006"],"arxiv":["1701.02956"]},"isi":1,"quality_controlled":"1","doi":"10.4171/jst/267","language":[{"iso":"eng"}]}]