[{"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0246-0203"]},"ec_funded":1,"issue":"3","volume":55,"oa_version":"Preprint","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<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."}],"intvolume":" 55","month":"09","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1710.02323"}],"scopus_import":"1","date_updated":"2023-10-17T08:53:45Z","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"_id":"72","status":"public","article_type":"original","type":"journal_article","publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","day":"25","year":"2019","isi":1,"date_created":"2018-12-11T11:44:29Z","doi":"10.1214/18-AIHP916","date_published":"2019-09-25T00:00:00Z","page":"1203-1225","oa":1,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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.","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.","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.","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","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","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.","short":"P. Ferrari, P. Ghosal, P. Nejjar, Annales de l’institut Henri Poincare (B) Probability and Statistics 55 (2019) 1203–1225."},"title":"Limit law of a second class particle in TASEP with non-random initial condition","external_id":{"isi":["000487763200001"],"arxiv":["1710.02323"]},"article_processing_charge":"No","author":[{"last_name":"Ferrari","full_name":"Ferrari, Patrick","first_name":"Patrick"},{"last_name":"Ghosal","full_name":"Ghosal, Promit","first_name":"Promit"},{"id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","first_name":"Peter","full_name":"Nejjar, Peter","last_name":"Nejjar"}],"project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"}]},{"title":"Location of the spectrum of Kronecker random matrices","article_processing_charge":"No","external_id":{"isi":["000467793600003"],"arxiv":["1706.08343"]},"author":[{"last_name":"Alt","full_name":"Alt, Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","first_name":"Johannes"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","last_name":"Krüger","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H"},{"orcid":"0000-0002-7327-856X","full_name":"Nemish, Yuriy","last_name":"Nemish","first_name":"Yuriy","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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","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","short":"J. Alt, L. Erdös, T.H. Krüger, Y. Nemish, Annales de l’institut Henri Poincare 55 (2019) 661–696.","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.","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.","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."},"project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"date_created":"2019-04-08T14:05:04Z","date_published":"2019-05-01T00:00:00Z","doi":"10.1214/18-AIHP894","page":"661-696","publication":"Annales de l'institut Henri Poincare","day":"01","year":"2019","isi":1,"oa":1,"publisher":"Institut Henri Poincaré","quality_controlled":"1","department":[{"_id":"LaEr"}],"date_updated":"2023-10-17T12:20:20Z","status":"public","type":"journal_article","_id":"6240","ec_funded":1,"related_material":{"record":[{"id":"149","status":"public","relation":"dissertation_contains"}]},"issue":"2","volume":55,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0246-0203"]},"intvolume":" 55","month":"05","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1706.08343"}],"scopus_import":"1","oa_version":"Preprint","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."}]},{"alternative_title":["ISTA Thesis"],"month":"03","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"}],"oa_version":"Published Version","related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"1144"},{"id":"6186","status":"public","relation":"part_of_dissertation"},{"status":"public","id":"6185","relation":"part_of_dissertation"},{"id":"6182","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"1012","status":"public"},{"id":"6184","status":"public","relation":"part_of_dissertation"}]},"ec_funded":1,"publication_identifier":{"issn":["2663-337X"]},"degree_awarded":"PhD","publication_status":"published","file":[{"date_created":"2019-03-28T08:53:52Z","file_name":"2019_Schroeder_Thesis.tar.gz","date_updated":"2020-07-14T12:47:21Z","file_size":7104482,"creator":"dernst","checksum":"6926f66f28079a81c4937e3764be00fc","file_id":"6180","content_type":"application/x-gzip","access_level":"closed","relation":"source_file"},{"creator":"dernst","date_updated":"2020-07-14T12:47:21Z","file_size":4228794,"date_created":"2019-03-28T08:53:52Z","file_name":"2019_Schroeder_Thesis.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"7d0ebb8d1207e89768cdd497a5bf80fb","file_id":"6181"}],"language":[{"iso":"eng"}],"type":"dissertation","status":"public","_id":"6179","file_date_updated":"2020-07-14T12:47:21Z","department":[{"_id":"LaEr"}],"supervisor":[{"last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"}],"date_updated":"2024-02-22T14:34:33Z","ddc":["515","519"],"publisher":"Institute of Science and Technology Austria","oa":1,"page":"375","doi":"10.15479/AT:ISTA:th6179","date_published":"2019-03-18T00:00:00Z","date_created":"2019-03-28T08:58:59Z","has_accepted_license":"1","year":"2019","day":"18","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"author":[{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder"}],"article_processing_charge":"No","title":"From Dyson to Pearcey: Universal statistics in random matrix theory","citation":{"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.","ista":"Schröder DJ. 2019. From Dyson to Pearcey: Universal statistics in random matrix theory. Institute of Science and Technology Austria.","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.","ama":"Schröder DJ. From Dyson to Pearcey: Universal statistics in random matrix theory. 2019. doi:10.15479/AT:ISTA:th6179","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","short":"D.J. Schröder, From Dyson to Pearcey: Universal Statistics in Random Matrix Theory, Institute of Science and Technology Austria, 2019.","ieee":"D. J. Schröder, “From Dyson to Pearcey: Universal statistics in random matrix theory,” Institute of Science and Technology Austria, 2019."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1"},{"publication":"Probability Theory and Related Fields","day":"14","year":"2018","date_created":"2018-12-11T11:47:56Z","doi":"10.1007/s00440-017-0787-8","date_published":"2018-06-14T00:00:00Z","oa":1,"publisher":"Springer","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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","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","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.","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.","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.","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."},"title":"Local law and Tracy–Widom limit for sparse random matrices","external_id":{"arxiv":["1605.08767"]},"author":[{"first_name":"Jii","full_name":"Lee, Jii","last_name":"Lee"},{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin","last_name":"Schnelli","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin"}],"publist_id":"7017","article_number":"543-616","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"language":[{"iso":"eng"}],"publication_status":"published","ec_funded":1,"volume":171,"issue":"1-2","oa_version":"Preprint","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"}],"intvolume":" 171","month":"06","main_file_link":[{"url":"https://arxiv.org/abs/1605.08767","open_access":"1"}],"scopus_import":1,"date_updated":"2021-01-12T08:09:33Z","department":[{"_id":"LaEr"}],"_id":"690","status":"public","type":"journal_article"},{"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"}],"oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1612.07776 ","open_access":"1"}],"scopus_import":"1","intvolume":" 28","month":"03","publication_status":"published","language":[{"iso":"eng"}],"ec_funded":1,"related_material":{"record":[{"id":"149","status":"public","relation":"dissertation_contains"}]},"issue":"1","volume":28,"_id":"566","type":"journal_article","article_type":"original","status":"public","date_updated":"2023-09-13T08:47:52Z","department":[{"_id":"LaEr"}],"oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","year":"2018","isi":1,"publication":"Annals Applied Probability ","day":"03","page":"148-203","date_created":"2018-12-11T11:47:13Z","date_published":"2018-03-03T00:00:00Z","doi":"10.1214/17-AAP1302","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"citation":{"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.","ama":"Alt J, Erdös L, Krüger TH. Local inhomogeneous circular law. Annals Applied Probability . 2018;28(1):148-203. doi:10.1214/17-AAP1302","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.","short":"J. Alt, L. Erdös, T.H. Krüger, Annals Applied Probability 28 (2018) 148–203.","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.","ista":"Alt J, Erdös L, Krüger TH. 2018. Local inhomogeneous circular law. Annals Applied Probability . 28(1), 148–203."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","external_id":{"arxiv":["1612.07776 "],"isi":["000431721800005"]},"article_processing_charge":"No","author":[{"last_name":"Alt","full_name":"Alt, Johannes","first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"last_name":"Krüger","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87"}],"title":"Local inhomogeneous circular law"}]