[{"issue":"3","abstract":[{"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<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.","lang":"eng"}],"type":"journal_article","oa_version":"Preprint","intvolume":" 55","status":"public","title":"Limit law of a second class particle in TASEP with non-random initial condition","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"72","article_processing_charge":"No","day":"25","scopus_import":"1","date_published":"2019-09-25T00:00:00Z","page":"1203-1225","article_type":"original","citation":{"chicago":"Ferrari, Patrick, Promit Ghosal, and Peter Nejjar. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics, 2019. https://doi.org/10.1214/18-AIHP916.","mla":"Ferrari, Patrick, et al. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 55, no. 3, Institute of Mathematical Statistics, 2019, pp. 1203–25, doi:10.1214/18-AIHP916.","short":"P. Ferrari, P. Ghosal, P. Nejjar, Annales de l’institut Henri Poincare (B) Probability and Statistics 55 (2019) 1203–1225.","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,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 55, no. 3. Institute of Mathematical Statistics, pp. 1203–1225, 2019.","apa":"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. Institute of Mathematical Statistics. https://doi.org/10.1214/18-AIHP916","ama":"Ferrari P, Ghosal P, Nejjar P. Limit law of a second class particle in TASEP with non-random initial condition. Annales de l’institut Henri Poincare (B) Probability and Statistics. 2019;55(3):1203-1225. doi:10.1214/18-AIHP916"},"publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","ec_funded":1,"volume":55,"date_updated":"2023-10-17T08:53:45Z","date_created":"2018-12-11T11:44:29Z","author":[{"full_name":"Ferrari, Patrick","first_name":"Patrick","last_name":"Ferrari"},{"first_name":"Promit","last_name":"Ghosal","full_name":"Ghosal, Promit"},{"full_name":"Nejjar, Peter","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","last_name":"Nejjar","first_name":"Peter"}],"publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"publication_status":"published","year":"2019","publication_identifier":{"issn":["0246-0203"]},"month":"09","language":[{"iso":"eng"}],"doi":"10.1214/18-AIHP916","project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","isi":1,"oa":1,"external_id":{"isi":["000487763200001"],"arxiv":["1710.02323"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1710.02323"}]},{"month":"05","publication_identifier":{"issn":["0246-0203"]},"isi":1,"quality_controlled":"1","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1706.08343","open_access":"1"}],"external_id":{"arxiv":["1706.08343"],"isi":["000467793600003"]},"language":[{"iso":"eng"}],"doi":"10.1214/18-AIHP894","ec_funded":1,"publication_status":"published","publisher":"Institut Henri Poincaré","department":[{"_id":"LaEr"}],"year":"2019","date_created":"2019-04-08T14:05:04Z","date_updated":"2023-10-17T12:20:20Z","volume":55,"author":[{"last_name":"Alt","first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","full_name":"Alt, Johannes"},{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"last_name":"Krüger","first_name":"Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H"},{"full_name":"Nemish, Yuriy","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7327-856X","first_name":"Yuriy","last_name":"Nemish"}],"related_material":{"record":[{"id":"149","status":"public","relation":"dissertation_contains"}]},"scopus_import":"1","day":"01","article_processing_charge":"No","page":"661-696","publication":"Annales de l'institut Henri Poincare","citation":{"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.","apa":"Alt, J., Erdös, L., Krüger, T. H., & Nemish, Y. (2019). Location of the spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare. Institut Henri Poincaré. https://doi.org/10.1214/18-AIHP894","ieee":"J. Alt, L. Erdös, T. H. Krüger, and Y. Nemish, “Location of the spectrum of Kronecker random matrices,” Annales de l’institut Henri Poincare, vol. 55, no. 2. Institut Henri Poincaré, pp. 661–696, 2019.","ama":"Alt J, Erdös L, Krüger TH, Nemish Y. Location of the spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare. 2019;55(2):661-696. doi:10.1214/18-AIHP894","chicago":"Alt, Johannes, László Erdös, Torben H Krüger, and Yuriy Nemish. “Location of the Spectrum of Kronecker Random Matrices.” Annales de l’institut Henri Poincare. Institut Henri Poincaré, 2019. https://doi.org/10.1214/18-AIHP894.","mla":"Alt, Johannes, et al. “Location of the Spectrum of Kronecker Random Matrices.” Annales de l’institut Henri Poincare, vol. 55, no. 2, Institut Henri Poincaré, 2019, pp. 661–96, doi:10.1214/18-AIHP894.","short":"J. Alt, L. Erdös, T.H. Krüger, Y. Nemish, Annales de l’institut Henri Poincare 55 (2019) 661–696."},"date_published":"2019-05-01T00:00:00Z","type":"journal_article","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."}],"issue":"2","title":"Location of the spectrum of Kronecker random matrices","status":"public","intvolume":" 55","_id":"6240","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint"},{"ec_funded":1,"file_date_updated":"2020-07-14T12:47:21Z","year":"2019","publisher":"Institute of Science and Technology Austria","department":[{"_id":"LaEr"}],"publication_status":"published","related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"1144"},{"id":"6186","status":"public","relation":"part_of_dissertation"},{"status":"public","relation":"part_of_dissertation","id":"6185"},{"id":"6182","status":"public","relation":"part_of_dissertation"},{"id":"1012","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"6184"}]},"author":[{"full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","first_name":"Dominik J","last_name":"Schröder"}],"date_updated":"2024-02-22T14:34:33Z","date_created":"2019-03-28T08:58:59Z","publication_identifier":{"issn":["2663-337X"]},"month":"03","oa":1,"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"doi":"10.15479/AT:ISTA:th6179","language":[{"iso":"eng"}],"degree_awarded":"PhD","supervisor":[{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"}],"type":"dissertation","alternative_title":["ISTA Thesis"],"abstract":[{"lang":"eng","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."}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"6179","ddc":["515","519"],"status":"public","title":"From Dyson to Pearcey: Universal statistics in random matrix theory","file":[{"content_type":"application/x-gzip","file_size":7104482,"creator":"dernst","file_name":"2019_Schroeder_Thesis.tar.gz","access_level":"closed","date_created":"2019-03-28T08:53:52Z","date_updated":"2020-07-14T12:47:21Z","checksum":"6926f66f28079a81c4937e3764be00fc","relation":"source_file","file_id":"6180"},{"file_name":"2019_Schroeder_Thesis.pdf","access_level":"open_access","content_type":"application/pdf","file_size":4228794,"creator":"dernst","relation":"main_file","file_id":"6181","date_updated":"2020-07-14T12:47:21Z","date_created":"2019-03-28T08:53:52Z","checksum":"7d0ebb8d1207e89768cdd497a5bf80fb"}],"oa_version":"Published Version","article_processing_charge":"No","has_accepted_license":"1","day":"18","citation":{"mla":"Schröder, Dominik J. From Dyson to Pearcey: Universal Statistics in Random Matrix Theory. Institute of Science and Technology Austria, 2019, doi:10.15479/AT:ISTA:th6179.","short":"D.J. Schröder, From Dyson to Pearcey: Universal Statistics in Random Matrix Theory, Institute of Science and Technology Austria, 2019.","chicago":"Schröder, Dominik J. “From Dyson to Pearcey: Universal Statistics in Random Matrix Theory.” Institute of Science and Technology Austria, 2019. https://doi.org/10.15479/AT:ISTA:th6179.","ama":"Schröder DJ. From Dyson to Pearcey: Universal statistics in random matrix theory. 2019. doi:10.15479/AT:ISTA:th6179","ista":"Schröder DJ. 2019. From Dyson to Pearcey: Universal statistics in random matrix theory. Institute of Science and Technology Austria.","apa":"Schröder, D. J. (2019). From Dyson to Pearcey: Universal statistics in random matrix theory. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th6179","ieee":"D. J. Schröder, “From Dyson to Pearcey: Universal statistics in random matrix theory,” Institute of Science and Technology Austria, 2019."},"page":"375","date_published":"2019-03-18T00:00:00Z"},{"day":"14","scopus_import":1,"date_published":"2018-06-14T00:00:00Z","publication":"Probability Theory and Related Fields","citation":{"short":"J. Lee, K. Schnelli, Probability Theory and Related Fields 171 (2018).","mla":"Lee, Jii, and Kevin Schnelli. “Local Law and Tracy–Widom Limit for Sparse Random Matrices.” Probability Theory and Related Fields, vol. 171, no. 1–2, 543–616, Springer, 2018, doi:10.1007/s00440-017-0787-8.","chicago":"Lee, Jii, and Kevin Schnelli. “Local Law and Tracy–Widom Limit for Sparse Random Matrices.” Probability Theory and Related Fields. Springer, 2018. https://doi.org/10.1007/s00440-017-0787-8.","ama":"Lee J, Schnelli K. Local law and Tracy–Widom limit for sparse random matrices. Probability Theory and Related Fields. 2018;171(1-2). doi:10.1007/s00440-017-0787-8","apa":"Lee, J., & Schnelli, K. (2018). Local law and Tracy–Widom limit for sparse random matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-017-0787-8","ieee":"J. Lee and K. Schnelli, “Local law and Tracy–Widom limit for sparse random matrices,” Probability Theory and Related Fields, 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."},"abstract":[{"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.","lang":"eng"}],"issue":"1-2","type":"journal_article","oa_version":"Preprint","title":"Local law and Tracy–Widom limit for sparse random matrices","status":"public","intvolume":" 171","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"690","month":"06","language":[{"iso":"eng"}],"doi":"10.1007/s00440-017-0787-8","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":["1605.08767"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1605.08767"}],"publist_id":"7017","ec_funded":1,"article_number":"543-616","date_created":"2018-12-11T11:47:56Z","date_updated":"2021-01-12T08:09:33Z","volume":171,"author":[{"full_name":"Lee, Jii","last_name":"Lee","first_name":"Jii"},{"full_name":"Schnelli, Kevin","orcid":"0000-0003-0954-3231","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","last_name":"Schnelli","first_name":"Kevin"}],"publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Springer","year":"2018"},{"publication_status":"published","publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"year":"2018","date_created":"2018-12-11T11:47:13Z","date_updated":"2023-09-13T08:47:52Z","volume":28,"author":[{"full_name":"Alt, Johannes","last_name":"Alt","first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","full_name":"Erdös, László"},{"orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","last_name":"Krüger","first_name":"Torben H","full_name":"Krüger, Torben H"}],"related_material":{"record":[{"id":"149","relation":"dissertation_contains","status":"public"}]},"ec_funded":1,"isi":1,"quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"oa":1,"external_id":{"arxiv":["1612.07776 "],"isi":["000431721800005"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1612.07776 "}],"language":[{"iso":"eng"}],"doi":"10.1214/17-AAP1302","month":"03","status":"public","title":"Local inhomogeneous circular law","intvolume":" 28","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"566","oa_version":"Preprint","type":"journal_article","abstract":[{"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","lang":"eng"}],"issue":"1","article_type":"original","page":"148-203","publication":"Annals Applied Probability ","citation":{"apa":"Alt, J., Erdös, L., & Krüger, T. H. (2018). Local inhomogeneous circular law. Annals Applied Probability . Institute of Mathematical Statistics. https://doi.org/10.1214/17-AAP1302","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “Local inhomogeneous circular law,” Annals Applied Probability , vol. 28, no. 1. Institute of Mathematical Statistics, pp. 148–203, 2018.","ista":"Alt J, Erdös L, Krüger TH. 2018. Local inhomogeneous circular law. Annals Applied Probability . 28(1), 148–203.","ama":"Alt J, Erdös L, Krüger TH. Local inhomogeneous circular law. Annals Applied Probability . 2018;28(1):148-203. doi:10.1214/17-AAP1302","chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “Local Inhomogeneous Circular Law.” Annals Applied Probability . Institute of Mathematical Statistics, 2018. https://doi.org/10.1214/17-AAP1302.","short":"J. Alt, L. Erdös, T.H. Krüger, Annals Applied Probability 28 (2018) 148–203.","mla":"Alt, Johannes, et al. “Local Inhomogeneous Circular Law.” Annals Applied Probability , vol. 28, no. 1, Institute of Mathematical Statistics, 2018, pp. 148–203, doi:10.1214/17-AAP1302."},"date_published":"2018-03-03T00:00:00Z","scopus_import":"1","day":"03","article_processing_charge":"No"},{"acknowledgement":"The work of the second author was also partially supported by the Hausdorff Center of Mathematics.","year":"2018","publication_status":"published","publisher":"Society for Industrial and Applied Mathematics ","department":[{"_id":"LaEr"}],"author":[{"full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"full_name":"Krüger, Torben H","first_name":"Torben H","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297"},{"full_name":"Renfrew, David T","first_name":"David T","last_name":"Renfrew","id":"4845BF6A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3493-121X"}],"date_created":"2018-12-11T11:45:03Z","date_updated":"2023-09-15T12:05:52Z","volume":50,"publist_id":"7740","ec_funded":1,"external_id":{"isi":["000437018500032"],"arxiv":["1708.01546"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.01546"}],"oa":1,"isi":1,"quality_controlled":"1","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"},{"name":"Structured Non-Hermitian Random Matrices","call_identifier":"FWF","_id":"258F40A4-B435-11E9-9278-68D0E5697425","grant_number":"M02080"}],"doi":"10.1137/17M1143125","language":[{"iso":"eng"}],"month":"01","_id":"181","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","title":"Power law decay for systems of randomly coupled differential equations","status":"public","intvolume":" 50","oa_version":"Published Version","type":"journal_article","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."}],"issue":"3","publication":"SIAM Journal on Mathematical Analysis","citation":{"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.","apa":"Erdös, L., Krüger, T. H., & Renfrew, D. T. (2018). Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/17M1143125","ieee":"L. Erdös, T. H. Krüger, and D. T. Renfrew, “Power law decay for systems of randomly coupled differential equations,” SIAM Journal on Mathematical Analysis, vol. 50, no. 3. Society for Industrial and Applied Mathematics , pp. 3271–3290, 2018.","ama":"Erdös L, Krüger TH, Renfrew DT. Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. 2018;50(3):3271-3290. doi:10.1137/17M1143125","chicago":"Erdös, László, Torben H Krüger, and David T Renfrew. “Power Law Decay for Systems of Randomly Coupled Differential Equations.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/17M1143125.","mla":"Erdös, László, et al. “Power Law Decay for Systems of Randomly Coupled Differential Equations.” SIAM Journal on Mathematical Analysis, vol. 50, no. 3, Society for Industrial and Applied Mathematics , 2018, pp. 3271–90, doi:10.1137/17M1143125.","short":"L. Erdös, T.H. Krüger, D.T. Renfrew, SIAM Journal on Mathematical Analysis 50 (2018) 3271–3290."},"page":"3271 - 3290","date_published":"2018-01-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No"},{"abstract":[{"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.","lang":"eng"}],"type":"journal_article","oa_version":"Preprint","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"5971","status":"public","title":"Bounds on the norm of Wigner-type random matrices","article_processing_charge":"No","day":"26","scopus_import":"1","date_published":"2018-09-26T00:00:00Z","citation":{"apa":"Erdös, L., & Mühlbacher, P. (2018). Bounds on the norm of Wigner-type random matrices. Random Matrices: Theory and Applications. World Scientific Publishing. https://doi.org/10.1142/s2010326319500096","ieee":"L. Erdös and P. Mühlbacher, “Bounds on the norm of Wigner-type random matrices,” Random matrices: Theory and applications. World Scientific Publishing, 2018.","ista":"Erdös L, Mühlbacher P. 2018. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications., 1950009.","ama":"Erdös L, Mühlbacher P. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications. 2018. doi:10.1142/s2010326319500096","chicago":"Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random Matrices.” Random Matrices: Theory and Applications. World Scientific Publishing, 2018. https://doi.org/10.1142/s2010326319500096.","short":"L. Erdös, P. Mühlbacher, Random Matrices: Theory and Applications (2018).","mla":"Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random Matrices.” Random Matrices: Theory and Applications, 1950009, World Scientific Publishing, 2018, doi:10.1142/s2010326319500096."},"publication":"Random matrices: Theory and applications","ec_funded":1,"article_number":"1950009","author":[{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"Mühlbacher, Peter","last_name":"Mühlbacher","first_name":"Peter"}],"date_created":"2019-02-13T10:40:54Z","date_updated":"2023-09-19T14:24:05Z","year":"2018","publisher":"World Scientific Publishing","department":[{"_id":"LaEr"}],"publication_status":"published","publication_identifier":{"eissn":["2010-3271"],"issn":["2010-3263"]},"month":"09","doi":"10.1142/s2010326319500096","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1802.05175","open_access":"1"}],"external_id":{"arxiv":["1802.05175"],"isi":["000477677200002"]},"oa":1,"project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"quality_controlled":"1","isi":1},{"author":[{"full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856"}],"related_material":{"record":[{"id":"6179","status":"public","relation":"dissertation_contains"}]},"date_updated":"2023-09-22T09:44:21Z","date_created":"2018-12-11T11:49:41Z","volume":2018,"year":"2018","publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Oxford University Press","ec_funded":1,"publist_id":"6383","doi":"10.1093/imrn/rnw330","language":[{"iso":"eng"}],"external_id":{"arxiv":["1608.05163"],"isi":["000441668300009"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1608.05163","open_access":"1"}],"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"}],"month":"05","publication_identifier":{"issn":["10737928"]},"oa_version":"Preprint","_id":"1012","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","title":"Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues","intvolume":" 2018","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"}],"issue":"10","type":"journal_article","date_published":"2018-05-18T00:00:00Z","publication":"International Mathematics Research Notices","citation":{"chicago":"Erdös, László, and Dominik J Schröder. “Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues.” International Mathematics Research Notices. Oxford University Press, 2018. https://doi.org/10.1093/imrn/rnw330.","mla":"Erdös, László, and Dominik J. Schröder. “Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues.” International Mathematics Research Notices, vol. 2018, no. 10, Oxford University Press, 2018, pp. 3255–98, doi:10.1093/imrn/rnw330.","short":"L. Erdös, D.J. Schröder, International Mathematics Research Notices 2018 (2018) 3255–3298.","ista":"Erdös L, Schröder DJ. 2018. Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. 2018(10), 3255–3298.","ieee":"L. Erdös and D. J. Schröder, “Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues,” International Mathematics Research Notices, vol. 2018, no. 10. Oxford University Press, pp. 3255–3298, 2018.","apa":"Erdös, L., & Schröder, D. J. (2018). Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnw330","ama":"Erdös L, Schröder DJ. Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. 2018;2018(10):3255-3298. doi:10.1093/imrn/rnw330"},"page":"3255-3298","day":"18","article_processing_charge":"No","scopus_import":"1"},{"doi":"10.30757/ALEA.v15-49","language":[{"iso":"eng"}],"external_id":{"isi":["000460475800022"],"arxiv":["1705.08836"]},"oa":1,"project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117"}],"isi":1,"quality_controlled":"1","publication_identifier":{"issn":["1980-0436"]},"month":"10","author":[{"full_name":"Nejjar, Peter","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","last_name":"Nejjar","first_name":"Peter"}],"volume":15,"date_updated":"2023-10-10T13:11:29Z","date_created":"2018-12-11T11:44:28Z","year":"2018","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"publisher":"Instituto Nacional de Matematica Pura e Aplicada","publication_status":"published","ec_funded":1,"file_date_updated":"2020-07-14T12:47:46Z","date_published":"2018-10-01T00:00:00Z","citation":{"ama":"Nejjar P. Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. 2018;15(2):1311-1334. doi:10.30757/ALEA.v15-49","apa":"Nejjar, P. (2018). Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. Instituto Nacional de Matematica Pura e Aplicada. https://doi.org/10.30757/ALEA.v15-49","ieee":"P. Nejjar, “Transition to shocks in TASEP and decoupling of last passage times,” Latin American Journal of Probability and Mathematical Statistics, vol. 15, no. 2. Instituto Nacional de Matematica Pura e Aplicada, pp. 1311–1334, 2018.","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.","short":"P. Nejjar, Latin American Journal of Probability and Mathematical Statistics 15 (2018) 1311–1334.","mla":"Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” Latin American Journal of Probability and Mathematical Statistics, vol. 15, no. 2, Instituto Nacional de Matematica Pura e Aplicada, 2018, pp. 1311–34, doi:10.30757/ALEA.v15-49.","chicago":"Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” Latin American Journal of Probability and Mathematical Statistics. Instituto Nacional de Matematica Pura e Aplicada, 2018. https://doi.org/10.30757/ALEA.v15-49."},"publication":"Latin American Journal of Probability and Mathematical Statistics","page":"1311-1334","article_type":"original","has_accepted_license":"1","article_processing_charge":"No","day":"01","scopus_import":"1","file":[{"creator":"kschuh","content_type":"application/pdf","file_size":394851,"access_level":"open_access","file_name":"2018_ALEA_Nejjar.pdf","checksum":"2ded46aa284a836a8cbb34133a64f1cb","date_created":"2019-02-14T09:44:10Z","date_updated":"2020-07-14T12:47:46Z","file_id":"5981","relation":"main_file"}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"70","intvolume":" 15","ddc":["510"],"title":"Transition to shocks in TASEP and decoupling of last passage times","status":"public","issue":"2","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"}],"type":"journal_article"},{"publication_identifier":{"issn":["0001-6969"],"eissn":["2064-8316"]},"month":"06","doi":"10.14232/actasm-018-753-y","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1802.03305","open_access":"1"}],"external_id":{"arxiv":["1802.03305"]},"project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"quality_controlled":"1","ec_funded":1,"publist_id":"7615","author":[{"last_name":"Virosztek","first_name":"Daniel","orcid":"0000-0003-1109-5511","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","full_name":"Virosztek, Daniel"}],"volume":84,"date_updated":"2023-10-16T10:29:22Z","date_created":"2018-12-11T11:45:36Z","year":"2018","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).","department":[{"_id":"LaEr"}],"publisher":"Springer Nature","publication_status":"published","article_processing_charge":"No","day":"04","scopus_import":"1","date_published":"2018-06-04T00:00:00Z","citation":{"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.","apa":"Virosztek, D. (2018). Maps on probability measures preserving certain distances - a survey and some new results. Acta Scientiarum Mathematicarum. Springer Nature. https://doi.org/10.14232/actasm-018-753-y","ieee":"D. Virosztek, “Maps on probability measures preserving certain distances - a survey and some new results,” Acta Scientiarum Mathematicarum, vol. 84, no. 1–2. Springer Nature, pp. 65–80, 2018.","ama":"Virosztek D. Maps on probability measures preserving certain distances - a survey and some new results. Acta Scientiarum Mathematicarum. 2018;84(1-2):65-80. doi:10.14232/actasm-018-753-y","chicago":"Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances - a Survey and Some New Results.” Acta Scientiarum Mathematicarum. Springer Nature, 2018. https://doi.org/10.14232/actasm-018-753-y.","mla":"Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances - a Survey and Some New Results.” Acta Scientiarum Mathematicarum, vol. 84, no. 1–2, Springer Nature, 2018, pp. 65–80, doi:10.14232/actasm-018-753-y.","short":"D. Virosztek, Acta Scientiarum Mathematicarum 84 (2018) 65–80."},"publication":"Acta Scientiarum Mathematicarum","page":"65 - 80","article_type":"original","issue":"1-2","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 >= 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"}],"type":"journal_article","oa_version":"Preprint","_id":"284","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 84","title":"Maps on probability measures preserving certain distances - a survey and some new results","status":"public"}]