--- _id: '72' 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. article_processing_charge: No article_type: original author: - first_name: Patrick full_name: Ferrari, Patrick last_name: Ferrari - first_name: Promit full_name: Ghosal, Promit last_name: Ghosal - first_name: Peter full_name: Nejjar, Peter id: 4BF426E2-F248-11E8-B48F-1D18A9856A87 last_name: Nejjar citation: 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 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. 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. 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. short: P. Ferrari, P. Ghosal, P. Nejjar, Annales de l’institut Henri Poincare (B) Probability and Statistics 55 (2019) 1203–1225. date_created: 2018-12-11T11:44:29Z date_published: 2019-09-25T00:00:00Z date_updated: 2023-10-17T08:53:45Z day: '25' department: - _id: LaEr - _id: JaMa doi: 10.1214/18-AIHP916 ec_funded: 1 external_id: arxiv: - '1710.02323' isi: - '000487763200001' intvolume: ' 55' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1710.02323 month: '09' oa: 1 oa_version: Preprint page: 1203-1225 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics publication: Annales de l'institut Henri Poincare (B) Probability and Statistics publication_identifier: issn: - 0246-0203 publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' scopus_import: '1' status: public title: Limit law of a second class particle in TASEP with non-random initial condition type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 55 year: '2019' ... --- _id: '6240' 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. article_processing_charge: No author: - first_name: Johannes full_name: Alt, Johannes id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87 last_name: Alt - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Torben H full_name: Krüger, Torben H id: 3020C786-F248-11E8-B48F-1D18A9856A87 last_name: Krüger orcid: 0000-0002-4821-3297 - first_name: Yuriy full_name: Nemish, Yuriy id: 4D902E6A-F248-11E8-B48F-1D18A9856A87 last_name: Nemish orcid: 0000-0002-7327-856X citation: 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 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 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. 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. 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. 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_created: 2019-04-08T14:05:04Z date_published: 2019-05-01T00:00:00Z date_updated: 2023-10-17T12:20:20Z day: '01' department: - _id: LaEr doi: 10.1214/18-AIHP894 ec_funded: 1 external_id: arxiv: - '1706.08343' isi: - '000467793600003' intvolume: ' 55' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1706.08343 month: '05' oa: 1 oa_version: Preprint page: 661-696 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Annales de l'institut Henri Poincare publication_identifier: issn: - 0246-0203 publication_status: published publisher: Institut Henri Poincaré quality_controlled: '1' related_material: record: - id: '149' relation: dissertation_contains status: public scopus_import: '1' status: public title: Location of the spectrum of Kronecker random matrices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 55 year: '2019' ... --- _id: '6179' 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." alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Dominik J full_name: Schröder, Dominik J id: 408ED176-F248-11E8-B48F-1D18A9856A87 last_name: Schröder orcid: 0000-0002-2904-1856 citation: 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' 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.' ieee: 'D. J. Schröder, “From Dyson to Pearcey: Universal statistics in random matrix theory,” Institute of Science and Technology Austria, 2019.' 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.' short: 'D.J. Schröder, From Dyson to Pearcey: Universal Statistics in Random Matrix Theory, Institute of Science and Technology Austria, 2019.' date_created: 2019-03-28T08:58:59Z date_published: 2019-03-18T00:00:00Z date_updated: 2024-02-22T14:34:33Z day: '18' ddc: - '515' - '519' degree_awarded: PhD department: - _id: LaEr doi: 10.15479/AT:ISTA:th6179 ec_funded: 1 file: - access_level: closed checksum: 6926f66f28079a81c4937e3764be00fc content_type: application/x-gzip creator: dernst date_created: 2019-03-28T08:53:52Z date_updated: 2020-07-14T12:47:21Z file_id: '6180' file_name: 2019_Schroeder_Thesis.tar.gz file_size: 7104482 relation: source_file - access_level: open_access checksum: 7d0ebb8d1207e89768cdd497a5bf80fb content_type: application/pdf creator: dernst date_created: 2019-03-28T08:53:52Z date_updated: 2020-07-14T12:47:21Z file_id: '6181' file_name: 2019_Schroeder_Thesis.pdf file_size: 4228794 relation: main_file file_date_updated: 2020-07-14T12:47:21Z has_accepted_license: '1' language: - iso: eng month: '03' oa: 1 oa_version: Published Version page: '375' project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '1144' relation: part_of_dissertation status: public - id: '6186' relation: part_of_dissertation status: public - id: '6185' relation: part_of_dissertation status: public - id: '6182' relation: part_of_dissertation status: public - id: '1012' relation: part_of_dissertation status: public - id: '6184' relation: part_of_dissertation status: public status: public supervisor: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 title: 'From Dyson to Pearcey: Universal statistics in random matrix theory' type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2019' ... --- _id: '690' abstract: - lang: eng text: We consider spectral properties and the edge universality of sparse random matrices, the class of random matrices that includes the adjacency matrices of the Erdős–Rényi graph model G(N, p). We prove a local law for the eigenvalue density up to the spectral edges. Under a suitable condition on the sparsity, we also prove that the rescaled extremal eigenvalues exhibit GOE Tracy–Widom fluctuations if a deterministic shift of the spectral edge due to the sparsity is included. For the adjacency matrix of the Erdős–Rényi graph this establishes the Tracy–Widom fluctuations of the second largest eigenvalue when p is much larger than N−2/3 with a deterministic shift of order (Np)−1. article_number: 543-616 author: - first_name: Jii full_name: Lee, Jii last_name: Lee - first_name: Kevin full_name: Schnelli, Kevin id: 434AD0AE-F248-11E8-B48F-1D18A9856A87 last_name: Schnelli orcid: 0000-0003-0954-3231 citation: 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 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. 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. 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. short: J. Lee, K. Schnelli, Probability Theory and Related Fields 171 (2018). date_created: 2018-12-11T11:47:56Z date_published: 2018-06-14T00:00:00Z date_updated: 2021-01-12T08:09:33Z day: '14' department: - _id: LaEr doi: 10.1007/s00440-017-0787-8 ec_funded: 1 external_id: arxiv: - '1605.08767' intvolume: ' 171' issue: 1-2 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1605.08767 month: '06' oa: 1 oa_version: Preprint project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Probability Theory and Related Fields publication_status: published publisher: Springer publist_id: '7017' quality_controlled: '1' scopus_import: 1 status: public title: Local law and Tracy–Widom limit for sparse random matrices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 171 year: '2018' ... --- _id: '566' 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" article_processing_charge: No article_type: original author: - first_name: Johannes full_name: Alt, Johannes id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87 last_name: Alt - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Torben H full_name: Krüger, Torben H id: 3020C786-F248-11E8-B48F-1D18A9856A87 last_name: Krüger orcid: 0000-0002-4821-3297 citation: 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 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. 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. 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. short: J. Alt, L. Erdös, T.H. Krüger, Annals Applied Probability 28 (2018) 148–203. date_created: 2018-12-11T11:47:13Z date_published: 2018-03-03T00:00:00Z date_updated: 2023-09-13T08:47:52Z day: '03' department: - _id: LaEr doi: 10.1214/17-AAP1302 ec_funded: 1 external_id: arxiv: - '1612.07776 ' isi: - '000431721800005' intvolume: ' 28' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: 'https://arxiv.org/abs/1612.07776 ' month: '03' oa: 1 oa_version: Preprint page: 148-203 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: 'Annals Applied Probability ' publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' related_material: record: - id: '149' relation: dissertation_contains status: public scopus_import: '1' status: public title: Local inhomogeneous circular law type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 28 year: '2018' ... --- _id: '181' 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. acknowledgement: The work of the second author was also partially supported by the Hausdorff Center of Mathematics. article_processing_charge: No author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Torben H full_name: Krüger, Torben H id: 3020C786-F248-11E8-B48F-1D18A9856A87 last_name: Krüger orcid: 0000-0002-4821-3297 - first_name: David T full_name: Renfrew, David T id: 4845BF6A-F248-11E8-B48F-1D18A9856A87 last_name: Renfrew orcid: 0000-0003-3493-121X citation: 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 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 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. 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. 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. 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. date_created: 2018-12-11T11:45:03Z date_published: 2018-01-01T00:00:00Z date_updated: 2023-09-15T12:05:52Z day: '01' department: - _id: LaEr doi: 10.1137/17M1143125 ec_funded: 1 external_id: arxiv: - '1708.01546' isi: - '000437018500032' intvolume: ' 50' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1708.01546 month: '01' oa: 1 oa_version: Published Version page: 3271 - 3290 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems - _id: 258F40A4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: M02080 name: Structured Non-Hermitian Random Matrices publication: SIAM Journal on Mathematical Analysis publication_status: published publisher: 'Society for Industrial and Applied Mathematics ' publist_id: '7740' quality_controlled: '1' scopus_import: '1' status: public title: Power law decay for systems of randomly coupled differential equations type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 50 year: '2018' ... --- _id: '5971' abstract: - lang: eng text: "We consider a Wigner-type ensemble, i.e. large hermitian N×N random matrices H=H∗ with centered independent entries and with a general matrix of variances Sxy=\U0001D53C∣∣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." article_number: '1950009' article_processing_charge: No author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Peter full_name: Mühlbacher, Peter last_name: Mühlbacher citation: ama: 'Erdös L, Mühlbacher P. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications. 2018. doi:10.1142/s2010326319500096' 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' 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.' 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.' 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.' short: 'L. Erdös, P. Mühlbacher, Random Matrices: Theory and Applications (2018).' date_created: 2019-02-13T10:40:54Z date_published: 2018-09-26T00:00:00Z date_updated: 2023-09-19T14:24:05Z day: '26' department: - _id: LaEr doi: 10.1142/s2010326319500096 ec_funded: 1 external_id: arxiv: - '1802.05175' isi: - '000477677200002' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1802.05175 month: '09' oa: 1 oa_version: Preprint project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: 'Random matrices: Theory and applications' publication_identifier: eissn: - 2010-3271 issn: - 2010-3263 publication_status: published publisher: World Scientific Publishing quality_controlled: '1' scopus_import: '1' status: public title: Bounds on the norm of Wigner-type random matrices type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2018' ... --- _id: '1012' abstract: - lang: eng 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. article_processing_charge: No author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Dominik J full_name: Schröder, Dominik J id: 408ED176-F248-11E8-B48F-1D18A9856A87 last_name: Schröder orcid: 0000-0002-2904-1856 citation: 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 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 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. 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. ista: Erdös L, Schröder DJ. 2018. Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. 2018(10), 3255–3298. mla: Erdös, László, and Dominik J. Schröder. “Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues.” 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. date_created: 2018-12-11T11:49:41Z date_published: 2018-05-18T00:00:00Z date_updated: 2023-09-22T09:44:21Z day: '18' department: - _id: LaEr doi: 10.1093/imrn/rnw330 ec_funded: 1 external_id: arxiv: - '1608.05163' isi: - '000441668300009' intvolume: ' 2018' isi: 1 issue: '10' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1608.05163 month: '05' oa: 1 oa_version: Preprint page: 3255-3298 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: International Mathematics Research Notices publication_identifier: issn: - '10737928' publication_status: published publisher: Oxford University Press publist_id: '6383' quality_controlled: '1' related_material: record: - id: '6179' relation: dissertation_contains status: public scopus_import: '1' status: public title: Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 2018 year: '2018' ... --- _id: '70' abstract: - lang: eng 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. article_processing_charge: No article_type: original author: - first_name: Peter full_name: Nejjar, Peter id: 4BF426E2-F248-11E8-B48F-1D18A9856A87 last_name: Nejjar 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 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. 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. 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. short: P. Nejjar, Latin American Journal of Probability and Mathematical Statistics 15 (2018) 1311–1334. date_created: 2018-12-11T11:44:28Z date_published: 2018-10-01T00:00:00Z date_updated: 2023-10-10T13:11:29Z day: '01' ddc: - '510' department: - _id: LaEr - _id: JaMa doi: 10.30757/ALEA.v15-49 ec_funded: 1 external_id: arxiv: - '1705.08836' isi: - '000460475800022' file: - access_level: open_access checksum: 2ded46aa284a836a8cbb34133a64f1cb content_type: application/pdf creator: kschuh date_created: 2019-02-14T09:44:10Z date_updated: 2020-07-14T12:47:46Z file_id: '5981' file_name: 2018_ALEA_Nejjar.pdf file_size: 394851 relation: main_file file_date_updated: 2020-07-14T12:47:46Z has_accepted_license: '1' intvolume: ' 15' isi: 1 issue: '2' language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 1311-1334 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics publication: Latin American Journal of Probability and Mathematical Statistics publication_identifier: issn: - 1980-0436 publication_status: published publisher: Instituto Nacional de Matematica Pura e Aplicada quality_controlled: '1' scopus_import: '1' status: public title: Transition to shocks in TASEP and decoupling of last passage times type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 15 year: '2018' ... --- _id: '284' abstract: - lang: eng 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." 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). article_processing_charge: No article_type: original author: - first_name: Daniel full_name: Virosztek, Daniel id: 48DB45DA-F248-11E8-B48F-1D18A9856A87 last_name: Virosztek orcid: 0000-0003-1109-5511 citation: 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 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 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. 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. 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. 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. date_created: 2018-12-11T11:45:36Z date_published: 2018-06-04T00:00:00Z date_updated: 2023-10-16T10:29:22Z day: '04' department: - _id: LaEr doi: 10.14232/actasm-018-753-y ec_funded: 1 external_id: arxiv: - '1802.03305' intvolume: ' 84' issue: 1-2 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1802.03305 month: '06' oa: 1 oa_version: Preprint page: 65 - 80 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Acta Scientiarum Mathematicarum publication_identifier: eissn: - 2064-8316 issn: - 0001-6969 publication_status: published publisher: Springer Nature publist_id: '7615' quality_controlled: '1' scopus_import: '1' status: public title: Maps on probability measures preserving certain distances - a survey and some new results type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 84 year: '2018' ... --- _id: '6183' abstract: - lang: eng text: "We study the unique solution $m$ of the Dyson equation \\[ -m(z)^{-1} = z - a\r\n+ S[m(z)] \\] on a von Neumann algebra $\\mathcal{A}$ with the constraint\r\n$\\mathrm{Im}\\,m\\geq 0$. Here, $z$ lies in the complex upper half-plane, $a$ is\r\na self-adjoint element of $\\mathcal{A}$ and $S$ is a positivity-preserving\r\nlinear operator on $\\mathcal{A}$. We show that $m$ is the Stieltjes transform\r\nof a compactly supported $\\mathcal{A}$-valued measure on $\\mathbb{R}$. Under\r\nsuitable assumptions, we establish that this measure has a uniformly\r\n$1/3$-H\\\"{o}lder continuous density with respect to the Lebesgue measure, which\r\nis supported on finitely many intervals, called bands. In fact, the density is\r\nanalytic inside the bands with a square-root growth at the edges and internal\r\ncubic root cusps whenever the gap between two bands vanishes. The shape of\r\nthese singularities is universal and no other singularity may occur. We give a\r\nprecise asymptotic description of $m$ near the singular points. These\r\nasymptotics generalize the analysis at the regular edges given in the companion\r\npaper on the Tracy-Widom universality for the edge eigenvalue statistics for\r\ncorrelated random matrices [arXiv:1804.07744] and they play a key role in the\r\nproof of the Pearcey universality at the cusp for Wigner-type matrices\r\n[arXiv:1809.03971,arXiv:1811.04055]. We also extend the finite dimensional band\r\nmass formula from [arXiv:1804.07744] to the von Neumann algebra setting by\r\nshowing that the spectral mass of the bands is topologically rigid under\r\ndeformations and we conclude that these masses are quantized in some important\r\ncases." article_number: '1804.07752' article_processing_charge: No author: - first_name: Johannes full_name: Alt, Johannes id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87 last_name: Alt - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Torben H full_name: Krüger, Torben H id: 3020C786-F248-11E8-B48F-1D18A9856A87 last_name: Krüger orcid: 0000-0002-4821-3297 citation: ama: 'Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral bands, edges and  cusps. arXiv.' apa: 'Alt, J., Erdös, L., & Krüger, T. H. (n.d.). The Dyson equation with linear self-energy: Spectral bands, edges and  cusps. arXiv.' chicago: 'Alt, Johannes, László Erdös, and Torben H Krüger. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and  Cusps.” ArXiv, n.d.' ieee: 'J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy: Spectral bands, edges and  cusps,” arXiv. .' ista: 'Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral bands, edges and  cusps. arXiv, 1804.07752.' mla: 'Alt, Johannes, et al. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and  Cusps.” ArXiv, 1804.07752.' short: J. Alt, L. Erdös, T.H. Krüger, ArXiv (n.d.). date_created: 2019-03-28T09:20:06Z date_published: 2018-04-20T00:00:00Z date_updated: 2023-12-18T10:46:08Z day: '20' department: - _id: LaEr external_id: arxiv: - '1804.07752' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1804.07752 month: '04' oa: 1 oa_version: Preprint publication: arXiv publication_status: submitted related_material: record: - id: '149' relation: dissertation_contains status: public - id: '14694' relation: later_version status: public status: public title: 'The Dyson equation with linear self-energy: Spectral bands, edges and cusps' type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2018' ... --- _id: '556' abstract: - lang: eng text: 'We investigate the free boundary Schur process, a variant of the Schur process introduced by Okounkov and Reshetikhin, where we allow the first and the last partitions to be arbitrary (instead of empty in the original setting). The pfaffian Schur process, previously studied by several authors, is recovered when just one of the boundary partitions is left free. We compute the correlation functions of the process in all generality via the free fermion formalism, which we extend with the thorough treatment of “free boundary states.” For the case of one free boundary, our approach yields a new proof that the process is pfaffian. For the case of two free boundaries, we find that the process is not pfaffian, but a closely related process is. We also study three different applications of the Schur process with one free boundary: fluctuations of symmetrized last passage percolation models, limit shapes and processes for symmetric plane partitions and for plane overpartitions.' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Dan full_name: Betea, Dan last_name: Betea - first_name: Jeremie full_name: Bouttier, Jeremie last_name: Bouttier - first_name: Peter full_name: Nejjar, Peter id: 4BF426E2-F248-11E8-B48F-1D18A9856A87 last_name: Nejjar - first_name: Mirjana full_name: Vuletic, Mirjana last_name: Vuletic citation: ama: Betea D, Bouttier J, Nejjar P, Vuletic M. The free boundary Schur process and applications I. Annales Henri Poincare. 2018;19(12):3663-3742. doi:10.1007/s00023-018-0723-1 apa: Betea, D., Bouttier, J., Nejjar, P., & Vuletic, M. (2018). The free boundary Schur process and applications I. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-018-0723-1 chicago: Betea, Dan, Jeremie Bouttier, Peter Nejjar, and Mirjana Vuletic. “The Free Boundary Schur Process and Applications I.” Annales Henri Poincare. Springer Nature, 2018. https://doi.org/10.1007/s00023-018-0723-1. ieee: D. Betea, J. Bouttier, P. Nejjar, and M. Vuletic, “The free boundary Schur process and applications I,” Annales Henri Poincare, vol. 19, no. 12. Springer Nature, pp. 3663–3742, 2018. ista: Betea D, Bouttier J, Nejjar P, Vuletic M. 2018. The free boundary Schur process and applications I. Annales Henri Poincare. 19(12), 3663–3742. mla: Betea, Dan, et al. “The Free Boundary Schur Process and Applications I.” Annales Henri Poincare, vol. 19, no. 12, Springer Nature, 2018, pp. 3663–742, doi:10.1007/s00023-018-0723-1. short: D. Betea, J. Bouttier, P. Nejjar, M. Vuletic, Annales Henri Poincare 19 (2018) 3663–3742. date_created: 2018-12-11T11:47:09Z date_published: 2018-11-13T00:00:00Z date_updated: 2024-02-20T10:48:17Z day: '13' ddc: - '500' department: - _id: LaEr - _id: JaMa doi: 10.1007/s00023-018-0723-1 ec_funded: 1 external_id: arxiv: - '1704.05809' file: - access_level: open_access checksum: 0c38abe73569b7166b7487ad5d23cc68 content_type: application/pdf creator: dernst date_created: 2019-01-21T15:18:55Z date_updated: 2020-07-14T12:47:03Z file_id: '5866' file_name: 2018_Annales_Betea.pdf file_size: 3084674 relation: main_file file_date_updated: 2020-07-14T12:47:03Z has_accepted_license: '1' intvolume: ' 19' issue: '12' language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 3663-3742 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics publication: Annales Henri Poincare publication_identifier: issn: - 1424-0637 publication_status: published publisher: Springer Nature publist_id: '7258' quality_controlled: '1' scopus_import: '1' status: public title: The free boundary Schur process and applications I tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 19 year: '2018' ... --- _id: '149' abstract: - lang: eng text: The eigenvalue density of many large random matrices is well approximated by a deterministic measure, the self-consistent density of states. In the present work, we show this behaviour for several classes of random matrices. In fact, we establish that, in each of these classes, the self-consistent density of states approximates the eigenvalue density of the random matrix on all scales slightly above the typical eigenvalue spacing. For large classes of random matrices, the self-consistent density of states exhibits several universal features. We prove that, under suitable assumptions, random Gram matrices and Hermitian random matrices with decaying correlations have a 1/3-Hölder continuous self-consistent density of states ρ on R, which is analytic, where it is positive, and has either a square root edge or a cubic root cusp, where it vanishes. We, thus, extend the validity of the corresponding result for Wigner-type matrices from [4, 5, 7]. We show that ρ is determined as the inverse Stieltjes transform of the normalized trace of the unique solution m(z) to the Dyson equation −m(z) −1 = z − a + S[m(z)] on C N×N with the constraint Im m(z) ≥ 0. Here, z lies in the complex upper half-plane, a is a self-adjoint element of C N×N and S is a positivity-preserving operator on C N×N encoding the first two moments of the random matrix. In order to analyze a possible limit of ρ for N → ∞ and address some applications in free probability theory, we also consider the Dyson equation on infinite dimensional von Neumann algebras. We present two applications to random matrices. We first establish that, under certain assumptions, large random matrices with independent entries have a rotationally symmetric self-consistent density of states which is supported on a centered disk in C. Moreover, it is infinitely often differentiable apart from a jump on the boundary of this disk. Second, we show edge universality at all regular (not necessarily extreme) spectral edges for Hermitian random matrices with decaying correlations. alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Johannes full_name: Alt, Johannes id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87 last_name: Alt citation: ama: Alt J. Dyson equation and eigenvalue statistics of random matrices. 2018. doi:10.15479/AT:ISTA:TH_1040 apa: Alt, J. (2018). Dyson equation and eigenvalue statistics of random matrices. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:TH_1040 chicago: Alt, Johannes. “Dyson Equation and Eigenvalue Statistics of Random Matrices.” Institute of Science and Technology Austria, 2018. https://doi.org/10.15479/AT:ISTA:TH_1040. ieee: J. Alt, “Dyson equation and eigenvalue statistics of random matrices,” Institute of Science and Technology Austria, 2018. ista: Alt J. 2018. Dyson equation and eigenvalue statistics of random matrices. Institute of Science and Technology Austria. mla: Alt, Johannes. Dyson Equation and Eigenvalue Statistics of Random Matrices. Institute of Science and Technology Austria, 2018, doi:10.15479/AT:ISTA:TH_1040. short: J. Alt, Dyson Equation and Eigenvalue Statistics of Random Matrices, Institute of Science and Technology Austria, 2018. date_created: 2018-12-11T11:44:53Z date_published: 2018-07-12T00:00:00Z date_updated: 2024-02-22T14:34:33Z day: '12' ddc: - '515' - '519' degree_awarded: PhD department: - _id: LaEr doi: 10.15479/AT:ISTA:TH_1040 ec_funded: 1 file: - access_level: open_access checksum: d4dad55a7513f345706aaaba90cb1bb8 content_type: application/pdf creator: dernst date_created: 2019-04-08T13:55:20Z date_updated: 2020-07-14T12:44:57Z file_id: '6241' file_name: 2018_thesis_Alt.pdf file_size: 5801709 relation: main_file - access_level: closed checksum: d73fcf46300dce74c403f2b491148ab4 content_type: application/zip creator: dernst date_created: 2019-04-08T13:55:20Z date_updated: 2020-07-14T12:44:57Z file_id: '6242' file_name: 2018_thesis_Alt_source.zip file_size: 3802059 relation: source_file file_date_updated: 2020-07-14T12:44:57Z has_accepted_license: '1' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: '456' project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria publist_id: '7772' pubrep_id: '1040' related_material: record: - id: '1677' relation: part_of_dissertation status: public - id: '550' relation: part_of_dissertation status: public - id: '6183' relation: part_of_dissertation status: public - id: '566' relation: part_of_dissertation status: public - id: '1010' relation: part_of_dissertation status: public - id: '6240' relation: part_of_dissertation status: public - id: '6184' relation: part_of_dissertation status: public status: public supervisor: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 title: Dyson equation and eigenvalue statistics of random matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: dissertation user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2018' ... --- _id: '483' abstract: - lang: eng text: We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, W ~ N. All previous results concerning universality of non-Gaussian random matrices are for mean-field models. By relying on a new mean-field reduction technique, we deduce universality from quantum unique ergodicity for band matrices. author: - first_name: Paul full_name: Bourgade, Paul last_name: Bourgade - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Horng full_name: Yau, Horng last_name: Yau - first_name: Jun full_name: Yin, Jun last_name: Yin citation: ama: Bourgade P, Erdös L, Yau H, Yin J. Universality for a class of random band matrices. Advances in Theoretical and Mathematical Physics. 2017;21(3):739-800. doi:10.4310/ATMP.2017.v21.n3.a5 apa: Bourgade, P., Erdös, L., Yau, H., & Yin, J. (2017). Universality for a class of random band matrices. Advances in Theoretical and Mathematical Physics. International Press. https://doi.org/10.4310/ATMP.2017.v21.n3.a5 chicago: Bourgade, Paul, László Erdös, Horng Yau, and Jun Yin. “Universality for a Class of Random Band Matrices.” Advances in Theoretical and Mathematical Physics. International Press, 2017. https://doi.org/10.4310/ATMP.2017.v21.n3.a5. ieee: P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Universality for a class of random band matrices,” Advances in Theoretical and Mathematical Physics, vol. 21, no. 3. International Press, pp. 739–800, 2017. ista: Bourgade P, Erdös L, Yau H, Yin J. 2017. Universality for a class of random band matrices. Advances in Theoretical and Mathematical Physics. 21(3), 739–800. mla: Bourgade, Paul, et al. “Universality for a Class of Random Band Matrices.” Advances in Theoretical and Mathematical Physics, vol. 21, no. 3, International Press, 2017, pp. 739–800, doi:10.4310/ATMP.2017.v21.n3.a5. short: P. Bourgade, L. Erdös, H. Yau, J. Yin, Advances in Theoretical and Mathematical Physics 21 (2017) 739–800. date_created: 2018-12-11T11:46:43Z date_published: 2017-08-25T00:00:00Z date_updated: 2021-01-12T08:00:57Z day: '25' department: - _id: LaEr doi: 10.4310/ATMP.2017.v21.n3.a5 ec_funded: 1 intvolume: ' 21' issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1602.02312 month: '08' oa: 1 oa_version: Submitted Version page: 739 - 800 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Advances in Theoretical and Mathematical Physics publication_identifier: issn: - '10950761' publication_status: published publisher: International Press publist_id: '7337' quality_controlled: '1' scopus_import: 1 status: public title: Universality for a class of random band matrices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 21 year: '2017' ... --- _id: '567' abstract: - lang: eng text: "This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality.\r\n" alternative_title: - Courant Lecture Notes article_processing_charge: No author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Horng full_name: Yau, Horng last_name: Yau citation: ama: Erdös L, Yau H. A Dynamical Approach to Random Matrix Theory. Vol 28. American Mathematical Society; 2017. doi:10.1090/cln/028 apa: Erdös, L., & Yau, H. (2017). A Dynamical Approach to Random Matrix Theory (Vol. 28). American Mathematical Society. https://doi.org/10.1090/cln/028 chicago: Erdös, László, and Horng Yau. A Dynamical Approach to Random Matrix Theory. Vol. 28. Courant Lecture Notes. American Mathematical Society, 2017. https://doi.org/10.1090/cln/028. ieee: L. Erdös and H. Yau, A Dynamical Approach to Random Matrix Theory, vol. 28. American Mathematical Society, 2017. ista: Erdös L, Yau H. 2017. A Dynamical Approach to Random Matrix Theory, American Mathematical Society, 226p. mla: Erdös, László, and Horng Yau. A Dynamical Approach to Random Matrix Theory. Vol. 28, American Mathematical Society, 2017, doi:10.1090/cln/028. short: L. Erdös, H. Yau, A Dynamical Approach to Random Matrix Theory, American Mathematical Society, 2017. date_created: 2018-12-11T11:47:13Z date_published: 2017-01-01T00:00:00Z date_updated: 2022-05-24T06:57:28Z day: '01' department: - _id: LaEr doi: 10.1090/cln/028 ec_funded: 1 intvolume: ' 28' language: - iso: eng month: '01' oa_version: None page: '226' project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication_identifier: eisbn: - 978-1-4704-4194-4 isbn: - 9-781-4704-3648-3 publication_status: published publisher: American Mathematical Society publist_id: '7247' quality_controlled: '1' series_title: Courant Lecture Notes status: public title: A Dynamical Approach to Random Matrix Theory type: book user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 28 year: '2017' ... --- _id: '615' abstract: - lang: eng text: We show that the Dyson Brownian Motion exhibits local universality after a very short time assuming that local rigidity and level repulsion of the eigenvalues hold. These conditions are verified, hence bulk spectral universality is proven, for a large class of Wigner-like matrices, including deformed Wigner ensembles and ensembles with non-stochastic variance matrices whose limiting densities differ from Wigner's semicircle law. author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Kevin full_name: Schnelli, Kevin id: 434AD0AE-F248-11E8-B48F-1D18A9856A87 last_name: Schnelli orcid: 0000-0003-0954-3231 citation: ama: Erdös L, Schnelli K. Universality for random matrix flows with time dependent density. Annales de l’institut Henri Poincare (B) Probability and Statistics. 2017;53(4):1606-1656. doi:10.1214/16-AIHP765 apa: Erdös, L., & Schnelli, K. (2017). Universality for random matrix flows with time dependent density. Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/16-AIHP765 chicago: Erdös, László, and Kevin Schnelli. “Universality for Random Matrix Flows with Time Dependent Density.” Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/16-AIHP765. ieee: L. Erdös and K. Schnelli, “Universality for random matrix flows with time dependent density,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 53, no. 4. Institute of Mathematical Statistics, pp. 1606–1656, 2017. ista: Erdös L, Schnelli K. 2017. Universality for random matrix flows with time dependent density. Annales de l’institut Henri Poincare (B) Probability and Statistics. 53(4), 1606–1656. mla: Erdös, László, and Kevin Schnelli. “Universality for Random Matrix Flows with Time Dependent Density.” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 53, no. 4, Institute of Mathematical Statistics, 2017, pp. 1606–56, doi:10.1214/16-AIHP765. short: L. Erdös, K. Schnelli, Annales de l’institut Henri Poincare (B) Probability and Statistics 53 (2017) 1606–1656. date_created: 2018-12-11T11:47:30Z date_published: 2017-11-01T00:00:00Z date_updated: 2021-01-12T08:06:22Z day: '01' department: - _id: LaEr doi: 10.1214/16-AIHP765 ec_funded: 1 intvolume: ' 53' issue: '4' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1504.00650 month: '11' oa: 1 oa_version: Submitted Version page: 1606 - 1656 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Annales de l'institut Henri Poincare (B) Probability and Statistics publication_identifier: issn: - '02460203' publication_status: published publisher: Institute of Mathematical Statistics publist_id: '7189' quality_controlled: '1' scopus_import: 1 status: public title: Universality for random matrix flows with time dependent density type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 53 year: '2017' ... --- _id: '721' abstract: - lang: eng text: 'Let S be a positivity-preserving symmetric linear operator acting on bounded functions. The nonlinear equation -1/m=z+Sm with a parameter z in the complex upper half-plane ℍ has a unique solution m with values in ℍ. We show that the z-dependence of this solution can be represented as the Stieltjes transforms of a family of probability measures v on ℝ. Under suitable conditions on S, we show that v has a real analytic density apart from finitely many algebraic singularities of degree at most 3. Our motivation comes from large random matrices. The solution m determines the density of eigenvalues of two prominent matrix ensembles: (i) matrices with centered independent entries whose variances are given by S and (ii) matrices with correlated entries with a translation-invariant correlation structure. Our analysis shows that the limiting eigenvalue density has only square root singularities or cubic root cusps; no other singularities occur.' author: - first_name: Oskari H full_name: Ajanki, Oskari H id: 36F2FB7E-F248-11E8-B48F-1D18A9856A87 last_name: Ajanki - first_name: Torben H full_name: Krüger, Torben H id: 3020C786-F248-11E8-B48F-1D18A9856A87 last_name: Krüger orcid: 0000-0002-4821-3297 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 citation: ama: Ajanki OH, Krüger TH, Erdös L. Singularities of solutions to quadratic vector equations on the complex upper half plane. Communications on Pure and Applied Mathematics. 2017;70(9):1672-1705. doi:10.1002/cpa.21639 apa: Ajanki, O. H., Krüger, T. H., & Erdös, L. (2017). Singularities of solutions to quadratic vector equations on the complex upper half plane. Communications on Pure and Applied Mathematics. Wiley-Blackwell. https://doi.org/10.1002/cpa.21639 chicago: Ajanki, Oskari H, Torben H Krüger, and László Erdös. “Singularities of Solutions to Quadratic Vector Equations on the Complex Upper Half Plane.” Communications on Pure and Applied Mathematics. Wiley-Blackwell, 2017. https://doi.org/10.1002/cpa.21639. ieee: O. H. Ajanki, T. H. Krüger, and L. Erdös, “Singularities of solutions to quadratic vector equations on the complex upper half plane,” Communications on Pure and Applied Mathematics, vol. 70, no. 9. Wiley-Blackwell, pp. 1672–1705, 2017. ista: Ajanki OH, Krüger TH, Erdös L. 2017. Singularities of solutions to quadratic vector equations on the complex upper half plane. Communications on Pure and Applied Mathematics. 70(9), 1672–1705. mla: Ajanki, Oskari H., et al. “Singularities of Solutions to Quadratic Vector Equations on the Complex Upper Half Plane.” Communications on Pure and Applied Mathematics, vol. 70, no. 9, Wiley-Blackwell, 2017, pp. 1672–705, doi:10.1002/cpa.21639. short: O.H. Ajanki, T.H. Krüger, L. Erdös, Communications on Pure and Applied Mathematics 70 (2017) 1672–1705. date_created: 2018-12-11T11:48:08Z date_published: 2017-09-01T00:00:00Z date_updated: 2021-01-12T08:12:24Z day: '01' department: - _id: LaEr doi: 10.1002/cpa.21639 ec_funded: 1 intvolume: ' 70' issue: '9' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1512.03703 month: '09' oa: 1 oa_version: Submitted Version page: 1672 - 1705 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Communications on Pure and Applied Mathematics publication_identifier: issn: - '00103640' publication_status: published publisher: Wiley-Blackwell publist_id: '6959' quality_controlled: '1' scopus_import: 1 status: public title: Singularities of solutions to quadratic vector equations on the complex upper half plane type: journal_article user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87 volume: 70 year: '2017' ... --- _id: '550' abstract: - lang: eng text: For large random matrices X with independent, centered entries but not necessarily identical variances, the eigenvalue density of XX* is well-approximated by a deterministic measure on ℝ. We show that the density of this measure has only square and cubic-root singularities away from zero. We also extend the bulk local law in [5] to the vicinity of these singularities. article_number: '63' author: - first_name: Johannes full_name: Alt, Johannes id: 36D3D8B6-F248-11E8-B48F-1D18A9856A87 last_name: Alt citation: ama: Alt J. Singularities of the density of states of random Gram matrices. Electronic Communications in Probability. 2017;22. doi:10.1214/17-ECP97 apa: Alt, J. (2017). Singularities of the density of states of random Gram matrices. Electronic Communications in Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/17-ECP97 chicago: Alt, Johannes. “Singularities of the Density of States of Random Gram Matrices.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/17-ECP97. ieee: J. Alt, “Singularities of the density of states of random Gram matrices,” Electronic Communications in Probability, vol. 22. Institute of Mathematical Statistics, 2017. ista: Alt J. 2017. Singularities of the density of states of random Gram matrices. Electronic Communications in Probability. 22, 63. mla: Alt, Johannes. “Singularities of the Density of States of Random Gram Matrices.” Electronic Communications in Probability, vol. 22, 63, Institute of Mathematical Statistics, 2017, doi:10.1214/17-ECP97. short: J. Alt, Electronic Communications in Probability 22 (2017). date_created: 2018-12-11T11:47:07Z date_published: 2017-11-21T00:00:00Z date_updated: 2023-09-07T12:38:08Z day: '21' ddc: - '539' department: - _id: LaEr doi: 10.1214/17-ECP97 ec_funded: 1 file: - access_level: open_access checksum: 0ec05303a0de190de145654237984c79 content_type: application/pdf creator: system date_created: 2018-12-12T10:08:04Z date_updated: 2020-07-14T12:47:00Z file_id: '4663' file_name: IST-2018-926-v1+1_euclid.ecp.1511233247.pdf file_size: 470876 relation: main_file file_date_updated: 2020-07-14T12:47:00Z has_accepted_license: '1' intvolume: ' 22' language: - iso: eng month: '11' oa: 1 oa_version: Published Version project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Electronic Communications in Probability publication_identifier: issn: - 1083589X publication_status: published publisher: Institute of Mathematical Statistics publist_id: '7265' pubrep_id: '926' quality_controlled: '1' related_material: record: - id: '149' relation: dissertation_contains status: public scopus_import: 1 status: public title: Singularities of the density of states of random Gram matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 22 year: '2017' ... --- _id: '1144' abstract: - lang: eng text: We show that matrix elements of functions of N × N Wigner matrices fluctuate on a scale of order N−1/2 and we identify the limiting fluctuation. Our result holds for any function f of the matrix that has bounded variation thus considerably relaxing the regularity requirement imposed in [7, 11]. acknowledgement: Partially supported by the IST Austria Excellence Scholarship. article_number: '86' author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Dominik J full_name: Schröder, Dominik J id: 408ED176-F248-11E8-B48F-1D18A9856A87 last_name: Schröder orcid: 0000-0002-2904-1856 citation: ama: Erdös L, Schröder DJ. Fluctuations of functions of Wigner matrices. Electronic Communications in Probability. 2017;21. doi:10.1214/16-ECP38 apa: Erdös, L., & Schröder, D. J. (2017). Fluctuations of functions of Wigner matrices. Electronic Communications in Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/16-ECP38 chicago: Erdös, László, and Dominik J Schröder. “Fluctuations of Functions of Wigner Matrices.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/16-ECP38. ieee: L. Erdös and D. J. Schröder, “Fluctuations of functions of Wigner matrices,” Electronic Communications in Probability, vol. 21. Institute of Mathematical Statistics, 2017. ista: Erdös L, Schröder DJ. 2017. Fluctuations of functions of Wigner matrices. Electronic Communications in Probability. 21, 86. mla: Erdös, László, and Dominik J. Schröder. “Fluctuations of Functions of Wigner Matrices.” Electronic Communications in Probability, vol. 21, 86, Institute of Mathematical Statistics, 2017, doi:10.1214/16-ECP38. short: L. Erdös, D.J. Schröder, Electronic Communications in Probability 21 (2017). date_created: 2018-12-11T11:50:23Z date_published: 2017-01-02T00:00:00Z date_updated: 2023-09-07T12:54:12Z day: '02' ddc: - '510' department: - _id: LaEr doi: 10.1214/16-ECP38 ec_funded: 1 file: - access_level: open_access content_type: application/pdf creator: system date_created: 2018-12-12T10:18:10Z date_updated: 2018-12-12T10:18:10Z file_id: '5329' file_name: IST-2017-747-v1+1_euclid.ecp.1483347665.pdf file_size: 440770 relation: main_file file_date_updated: 2018-12-12T10:18:10Z has_accepted_license: '1' intvolume: ' 21' language: - iso: eng month: '01' oa: 1 oa_version: Published Version project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Electronic Communications in Probability publication_status: published publisher: Institute of Mathematical Statistics publist_id: '6214' pubrep_id: '747' quality_controlled: '1' related_material: record: - id: '6179' relation: dissertation_contains status: public scopus_import: 1 status: public title: Fluctuations of functions of Wigner matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 21 year: '2017' ... --- _id: '1528' abstract: - lang: eng text: 'We consider N×N Hermitian random matrices H consisting of blocks of size M≥N6/7. The matrix elements are i.i.d. within the blocks, close to a Gaussian in the four moment matching sense, but their distribution varies from block to block to form a block-band structure, with an essential band width M. We show that the entries of the Green’s function G(z)=(H−z)−1 satisfy the local semicircle law with spectral parameter z=E+iη down to the real axis for any η≫N−1, using a combination of the supersymmetry method inspired by Shcherbina (J Stat Phys 155(3): 466–499, 2014) and the Green’s function comparison strategy. Previous estimates were valid only for η≫M−1. The new estimate also implies that the eigenvectors in the middle of the spectrum are fully delocalized.' acknowledgement: "Z. Bao was supported by ERC Advanced Grant RANMAT No. 338804; L. Erdős was partially supported by ERC Advanced Grant RANMAT No. 338804.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria). The authors are very grateful to the anonymous referees for careful reading and valuable comments, which helped to improve the organization." article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Zhigang full_name: Bao, Zhigang id: 442E6A6C-F248-11E8-B48F-1D18A9856A87 last_name: Bao orcid: 0000-0003-3036-1475 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 citation: ama: Bao Z, Erdös L. Delocalization for a class of random block band matrices. Probability Theory and Related Fields. 2017;167(3-4):673-776. doi:10.1007/s00440-015-0692-y apa: Bao, Z., & Erdös, L. (2017). Delocalization for a class of random block band matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-015-0692-y chicago: Bao, Zhigang, and László Erdös. “Delocalization for a Class of Random Block Band Matrices.” Probability Theory and Related Fields. Springer, 2017. https://doi.org/10.1007/s00440-015-0692-y. ieee: Z. Bao and L. Erdös, “Delocalization for a class of random block band matrices,” Probability Theory and Related Fields, vol. 167, no. 3–4. Springer, pp. 673–776, 2017. ista: Bao Z, Erdös L. 2017. Delocalization for a class of random block band matrices. Probability Theory and Related Fields. 167(3–4), 673–776. mla: Bao, Zhigang, and László Erdös. “Delocalization for a Class of Random Block Band Matrices.” Probability Theory and Related Fields, vol. 167, no. 3–4, Springer, 2017, pp. 673–776, doi:10.1007/s00440-015-0692-y. short: Z. Bao, L. Erdös, Probability Theory and Related Fields 167 (2017) 673–776. date_created: 2018-12-11T11:52:32Z date_published: 2017-04-01T00:00:00Z date_updated: 2023-09-20T09:42:12Z day: '01' ddc: - '530' department: - _id: LaEr doi: 10.1007/s00440-015-0692-y ec_funded: 1 external_id: isi: - '000398842700004' file: - access_level: open_access checksum: 67afa85ff1e220cbc1f9f477a828513c content_type: application/pdf creator: system date_created: 2018-12-12T10:08:05Z date_updated: 2020-07-14T12:45:00Z file_id: '4665' file_name: IST-2016-489-v1+1_s00440-015-0692-y.pdf file_size: 1615755 relation: main_file file_date_updated: 2020-07-14T12:45:00Z has_accepted_license: '1' intvolume: ' 167' isi: 1 issue: 3-4 language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: 673 - 776 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Probability Theory and Related Fields publication_identifier: issn: - '01788051' publication_status: published publisher: Springer publist_id: '5644' pubrep_id: '489' quality_controlled: '1' scopus_import: '1' status: public title: Delocalization for a class of random block band matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 167 year: '2017' ...