--- _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. article_processing_charge: No arxiv: 1 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. corr_author: '1' date_created: 2018-12-11T11:47:30Z date_published: 2017-11-01T00:00:00Z date_updated: 2025-09-11T07:32:50Z day: '01' department: - _id: LaEr doi: 10.1214/16-AIHP765 ec_funded: 1 external_id: arxiv: - '1504.00650' isi: - '000416376500005' intvolume: ' 53' isi: 1 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: - 0246-0203 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 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.' article_processing_charge: No arxiv: 1 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. 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, 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, 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, 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. corr_author: '1' date_created: 2018-12-11T11:48:08Z date_published: 2017-09-01T00:00:00Z date_updated: 2025-09-10T10:58:02Z day: '01' department: - _id: LaEr doi: 10.1002/cpa.21639 ec_funded: 1 external_id: arxiv: - '1512.03703' isi: - '000405752100002' intvolume: ' 70' isi: 1 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: - 0010-3640 publication_status: published publisher: Wiley 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 70 year: '2017' ... --- _id: '733' abstract: - lang: eng text: Let A and B be two N by N deterministic Hermitian matrices and let U be an N by N Haar distributed unitary matrix. It is well known that the spectral distribution of the sum H = A + UBU∗ converges weakly to the free additive convolution of the spectral distributions of A and B, as N tends to infinity. We establish the optimal convergence rate in the bulk of the spectrum. acknowledgement: Partially supported by ERC Advanced Grant RANMAT No. 338804, Hong Kong RGC grant ECS 26301517, and the Göran Gustafsson Foundation article_processing_charge: No arxiv: 1 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 - first_name: Kevin full_name: Schnelli, Kevin id: 434AD0AE-F248-11E8-B48F-1D18A9856A87 last_name: Schnelli orcid: 0000-0003-0954-3231 citation: ama: Bao Z, Erdös L, Schnelli K. Convergence rate for spectral distribution of addition of random matrices. Advances in Mathematics. 2017;319:251-291. doi:10.1016/j.aim.2017.08.028 apa: Bao, Z., Erdös, L., & Schnelli, K. (2017). Convergence rate for spectral distribution of addition of random matrices. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2017.08.028 chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Convergence Rate for Spectral Distribution of Addition of Random Matrices.” Advances in Mathematics. Academic Press, 2017. https://doi.org/10.1016/j.aim.2017.08.028. ieee: Z. Bao, L. Erdös, and K. Schnelli, “Convergence rate for spectral distribution of addition of random matrices,” Advances in Mathematics, vol. 319. Academic Press, pp. 251–291, 2017. ista: Bao Z, Erdös L, Schnelli K. 2017. Convergence rate for spectral distribution of addition of random matrices. Advances in Mathematics. 319, 251–291. mla: Bao, Zhigang, et al. “Convergence Rate for Spectral Distribution of Addition of Random Matrices.” Advances in Mathematics, vol. 319, Academic Press, 2017, pp. 251–91, doi:10.1016/j.aim.2017.08.028. short: Z. Bao, L. Erdös, K. Schnelli, Advances in Mathematics 319 (2017) 251–291. corr_author: '1' date_created: 2018-12-11T11:48:13Z date_published: 2017-10-15T00:00:00Z date_updated: 2025-06-04T10:13:45Z day: '15' department: - _id: LaEr doi: 10.1016/j.aim.2017.08.028 ec_funded: 1 external_id: arxiv: - '1606.03076' isi: - '000412150400010' intvolume: ' 319' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1606.03076 month: '10' oa: 1 oa_version: Submitted Version page: 251 - 291 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Advances in Mathematics publication_status: published publisher: Academic Press publist_id: '6935' quality_controlled: '1' scopus_import: '1' status: public title: Convergence rate for spectral distribution of addition of random matrices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 319 year: '2017' ... --- _id: '447' abstract: - lang: eng text: We consider last passage percolation (LPP) models with exponentially distributed random variables, which are linked to the totally asymmetric simple exclusion process (TASEP). The competition interface for LPP was introduced and studied in Ferrari and Pimentel (2005a) for cases where the corresponding exclusion process had a rarefaction fan. Here we consider situations with a shock and determine the law of the fluctuations of the competition interface around its deter- ministic law of large number position. We also study the multipoint distribution of the LPP around the shock, extending our one-point result of Ferrari and Nejjar (2015). article_processing_charge: No article_type: original author: - first_name: Patrik full_name: Ferrari, Patrik last_name: Ferrari - first_name: Peter full_name: Nejjar, Peter id: 4BF426E2-F248-11E8-B48F-1D18A9856A87 last_name: Nejjar citation: ama: Ferrari P, Nejjar P. Fluctuations of the competition interface in presence of shocks. Revista Latino-Americana de Probabilidade e Estatística. 2017;9:299-325. doi:10.30757/ALEA.v14-17 apa: Ferrari, P., & Nejjar, P. (2017). Fluctuations of the competition interface in presence of shocks. Revista Latino-Americana de Probabilidade e Estatística. Instituto Nacional de Matematica Pura e Aplicada. https://doi.org/10.30757/ALEA.v14-17 chicago: Ferrari, Patrik, and Peter Nejjar. “Fluctuations of the Competition Interface in Presence of Shocks.” Revista Latino-Americana de Probabilidade e Estatística. Instituto Nacional de Matematica Pura e Aplicada, 2017. https://doi.org/10.30757/ALEA.v14-17. ieee: P. Ferrari and P. Nejjar, “Fluctuations of the competition interface in presence of shocks,” Revista Latino-Americana de Probabilidade e Estatística, vol. 9. Instituto Nacional de Matematica Pura e Aplicada, pp. 299–325, 2017. ista: Ferrari P, Nejjar P. 2017. Fluctuations of the competition interface in presence of shocks. Revista Latino-Americana de Probabilidade e Estatística. 9, 299–325. mla: Ferrari, Patrik, and Peter Nejjar. “Fluctuations of the Competition Interface in Presence of Shocks.” Revista Latino-Americana de Probabilidade e Estatística, vol. 9, Instituto Nacional de Matematica Pura e Aplicada, 2017, pp. 299–325, doi:10.30757/ALEA.v14-17. short: P. Ferrari, P. Nejjar, Revista Latino-Americana de Probabilidade e Estatística 9 (2017) 299–325. corr_author: '1' date_created: 2018-12-11T11:46:31Z date_published: 2017-03-23T00:00:00Z date_updated: 2025-09-18T10:02:36Z day: '23' department: - _id: LaEr - _id: JaMa doi: 10.30757/ALEA.v14-17 ec_funded: 1 external_id: isi: - '000404011700017' intvolume: ' 9' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: http://alea.impa.br/articles/v14/14-17.pdf month: '03' oa: 1 oa_version: Submitted Version page: 299 - 325 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Revista Latino-Americana de Probabilidade e Estatística publication_status: published publisher: Instituto Nacional de Matematica Pura e Aplicada publist_id: '7376' quality_controlled: '1' scopus_import: '1' status: public title: Fluctuations of the competition interface in presence of shocks type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 9 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' 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 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: 2026-04-08T13:55:03Z day: '02' ddc: - '510' department: - _id: LaEr doi: 10.1214/16-ECP38 ec_funded: 1 external_id: isi: - '000396604900037' 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' isi: 1 language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 21 year: '2017' ... --- _id: '1010' abstract: - lang: eng text: 'We prove a local law in the bulk of the spectrum for random Gram matrices XX∗, a generalization of sample covariance matrices, where X is a large matrix with independent, centered entries with arbitrary variances. The limiting eigenvalue density that generalizes the Marchenko-Pastur law is determined by solving a system of nonlinear equations. Our entrywise and averaged local laws are on the optimal scale with the optimal error bounds. They hold both in the square case (hard edge) and in the properly rectangular case (soft edge). In the latter case we also establish a macroscopic gap away from zero in the spectrum of XX∗. ' article_number: '25' article_processing_charge: No arxiv: 1 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 law for random Gram matrices. Electronic Journal of Probability. 2017;22. doi:10.1214/17-EJP42 apa: Alt, J., Erdös, L., & Krüger, T. H. (2017). Local law for random Gram matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/17-EJP42 chicago: Alt, Johannes, László Erdös, and Torben H Krüger. “Local Law for Random Gram Matrices.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/17-EJP42. ieee: J. Alt, L. Erdös, and T. H. Krüger, “Local law for random Gram matrices,” Electronic Journal of Probability, vol. 22. Institute of Mathematical Statistics, 2017. ista: Alt J, Erdös L, Krüger TH. 2017. Local law for random Gram matrices. Electronic Journal of Probability. 22, 25. mla: Alt, Johannes, et al. “Local Law for Random Gram Matrices.” Electronic Journal of Probability, vol. 22, 25, Institute of Mathematical Statistics, 2017, doi:10.1214/17-EJP42. short: J. Alt, L. Erdös, T.H. Krüger, Electronic Journal of Probability 22 (2017). date_created: 2018-12-11T11:49:40Z date_published: 2017-03-08T00:00:00Z date_updated: 2026-04-08T14:11:36Z day: '08' ddc: - '510' - '539' department: - _id: LaEr doi: 10.1214/17-EJP42 ec_funded: 1 external_id: arxiv: - '1606.07353' isi: - '000396611900025' file: - access_level: open_access content_type: application/pdf creator: system date_created: 2018-12-12T10:13:39Z date_updated: 2018-12-12T10:13:39Z file_id: '5024' file_name: IST-2017-807-v1+1_euclid.ejp.1488942016.pdf file_size: 639384 relation: main_file file_date_updated: 2018-12-12T10:13:39Z has_accepted_license: '1' intvolume: ' 22' isi: 1 language: - iso: eng month: '03' 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 Journal of Probability publication_identifier: issn: - 1083-6489 publication_status: published publisher: Institute of Mathematical Statistics publist_id: '6386' pubrep_id: '807' quality_controlled: '1' related_material: record: - id: '149' relation: dissertation_contains status: public scopus_import: '1' status: public title: Local law for 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: '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' 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. 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). corr_author: '1' date_created: 2018-12-11T11:47:07Z date_published: 2017-11-21T00:00:00Z date_updated: 2026-04-08T14:11:36Z day: '21' ddc: - '539' department: - _id: LaEr doi: 10.1214/17-ECP97 ec_funded: 1 external_id: isi: - '000416389200001' 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' isi: 1 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: - 1083-589X 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 22 year: '2017' ... --- _id: '1337' abstract: - lang: eng text: We consider the local eigenvalue distribution of large self-adjoint N×N random matrices H=H∗ with centered independent entries. In contrast to previous works the matrix of variances sij=\mathbbmE|hij|2 is not assumed to be stochastic. Hence the density of states is not the Wigner semicircle law. Its possible shapes are described in the companion paper (Ajanki et al. in Quadratic Vector Equations on the Complex Upper Half Plane. arXiv:1506.05095). We show that as N grows, the resolvent, G(z)=(H−z)−1, converges to a diagonal matrix, diag(m(z)), where m(z)=(m1(z),…,mN(z)) solves the vector equation −1/mi(z)=z+∑jsijmj(z) that has been analyzed in Ajanki et al. (Quadratic Vector Equations on the Complex Upper Half Plane. arXiv:1506.05095). We prove a local law down to the smallest spectral resolution scale, and bulk universality for both real symmetric and complex hermitian symmetry classes. acknowledgement: 'Open access funding provided by Institute of Science and Technology (IST Austria). ' article_processing_charge: Yes (via OA deal) author: - first_name: Oskari H full_name: Ajanki, Oskari H id: 36F2FB7E-F248-11E8-B48F-1D18A9856A87 last_name: Ajanki - 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: Ajanki OH, Erdös L, Krüger TH. Universality for general Wigner-type matrices. Probability Theory and Related Fields. 2017;169(3-4):667-727. doi:10.1007/s00440-016-0740-2 apa: Ajanki, O. H., Erdös, L., & Krüger, T. H. (2017). Universality for general Wigner-type matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-016-0740-2 chicago: Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Universality for General Wigner-Type Matrices.” Probability Theory and Related Fields. Springer, 2017. https://doi.org/10.1007/s00440-016-0740-2. ieee: O. H. Ajanki, L. Erdös, and T. H. Krüger, “Universality for general Wigner-type matrices,” Probability Theory and Related Fields, vol. 169, no. 3–4. Springer, pp. 667–727, 2017. ista: Ajanki OH, Erdös L, Krüger TH. 2017. Universality for general Wigner-type matrices. Probability Theory and Related Fields. 169(3–4), 667–727. mla: Ajanki, Oskari H., et al. “Universality for General Wigner-Type Matrices.” Probability Theory and Related Fields, vol. 169, no. 3–4, Springer, 2017, pp. 667–727, doi:10.1007/s00440-016-0740-2. short: O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields 169 (2017) 667–727. corr_author: '1' date_created: 2018-12-11T11:51:27Z date_published: 2017-12-01T00:00:00Z date_updated: 2026-04-16T09:55:44Z day: '01' ddc: - '510' - '530' department: - _id: LaEr doi: 10.1007/s00440-016-0740-2 ec_funded: 1 external_id: isi: - '000414358400002' file: - access_level: open_access checksum: 29f5a72c3f91e408aeb9e78344973803 content_type: application/pdf creator: system date_created: 2018-12-12T10:08:25Z date_updated: 2020-07-14T12:44:44Z file_id: '4686' file_name: IST-2017-657-v1+2_s00440-016-0740-2.pdf file_size: 988843 relation: main_file file_date_updated: 2020-07-14T12:44:44Z has_accepted_license: '1' intvolume: ' 169' isi: 1 issue: 3-4 language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: 667 - 727 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Probability Theory and Related Fields publication_identifier: issn: - 0178-8051 publication_status: published publisher: Springer publist_id: '5930' pubrep_id: '657' quality_controlled: '1' scopus_import: '1' status: public title: Universality for general Wigner-type 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: ba8df636-2132-11f1-aed0-ed93e2281fdd volume: 169 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. corr_author: '1' date_created: 2018-12-11T11:52:32Z date_published: 2017-04-01T00:00:00Z date_updated: 2026-04-16T09:55:56Z 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: - 0178-8051 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: ba8df636-2132-11f1-aed0-ed93e2281fdd volume: 167 year: '2017' ... --- _id: '1157' abstract: - lang: eng text: We consider sample covariance matrices of the form Q = ( σ1/2X)(σ1/2X)∗, where the sample X is an M ×N random matrix whose entries are real independent random variables with variance 1/N and whereσ is an M × M positive-definite deterministic matrix. We analyze the asymptotic fluctuations of the largest rescaled eigenvalue of Q when both M and N tend to infinity with N/M →d ϵ (0,∞). For a large class of populations σ in the sub-critical regime, we show that the distribution of the largest rescaled eigenvalue of Q is given by the type-1 Tracy-Widom distribution under the additional assumptions that (1) either the entries of X are i.i.d. Gaussians or (2) that σ is diagonal and that the entries of X have a sub-exponential decay. acknowledgement: "We thank Horng-Tzer Yau for numerous discussions and remarks. We are grateful to Ben Adlam, Jinho Baik, Zhigang Bao, Paul Bourgade, László Erd ̋os, Iain Johnstone and Antti Knowles for comments. We are also grate-\r\nful to the anonymous referee for carefully reading our manuscript and suggesting several improvements." article_processing_charge: No arxiv: 1 author: - first_name: Ji full_name: Lee, Ji 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. Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population. Annals of Applied Probability. 2016;26(6):3786-3839. doi:10.1214/16-AAP1193 apa: Lee, J., & Schnelli, K. (2016). Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/16-AAP1193 chicago: Lee, Ji, and Kevin Schnelli. “Tracy-Widom Distribution for the Largest Eigenvalue of Real Sample Covariance Matrices with General Population.” Annals of Applied Probability. Institute of Mathematical Statistics, 2016. https://doi.org/10.1214/16-AAP1193. ieee: J. Lee and K. Schnelli, “Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population,” Annals of Applied Probability, vol. 26, no. 6. Institute of Mathematical Statistics, pp. 3786–3839, 2016. ista: Lee J, Schnelli K. 2016. Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population. Annals of Applied Probability. 26(6), 3786–3839. mla: Lee, Ji, and Kevin Schnelli. “Tracy-Widom Distribution for the Largest Eigenvalue of Real Sample Covariance Matrices with General Population.” Annals of Applied Probability, vol. 26, no. 6, Institute of Mathematical Statistics, 2016, pp. 3786–839, doi:10.1214/16-AAP1193. short: J. Lee, K. Schnelli, Annals of Applied Probability 26 (2016) 3786–3839. date_created: 2018-12-11T11:50:27Z date_published: 2016-12-15T00:00:00Z date_updated: 2025-09-22T09:55:43Z day: '15' department: - _id: LaEr doi: 10.1214/16-AAP1193 ec_funded: 1 external_id: arxiv: - '1409.4979' isi: - '000391240100016' intvolume: ' 26' isi: 1 issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1409.4979 month: '12' oa: 1 oa_version: Preprint page: 3786 - 3839 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Annals of Applied Probability publication_status: published publisher: Institute of Mathematical Statistics publist_id: '6201' quality_controlled: '1' scopus_import: '1' status: public title: Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 26 year: '2016' ... --- _id: '1219' abstract: - lang: eng text: We consider N×N random matrices of the form H = W + V where W is a real symmetric or complex Hermitian Wigner matrix and V is a random or deterministic, real, diagonal matrix whose entries are independent of W. We assume subexponential decay for the matrix entries of W, and we choose V so that the eigenvalues ofW and V are typically of the same order. For a large class of diagonal matrices V , we show that the local statistics in the bulk of the spectrum are universal in the limit of large N. acknowledgement: "J.C. was supported in part by National Research Foundation of Korea Grant 2011-0013474 and TJ Park Junior Faculty Fellowship.\r\nK.S. was supported by ERC Advanced Grant RANMAT, No. 338804, and the \"Fund for Math.\"\r\nB.S. was supported by NSF GRFP Fellowship DGE-1144152.\r\nH.Y. was supported in part by NSF Grant DMS-13-07444 and Simons investigator fellowship. We thank Paul Bourgade, László Erd ̋os and Antti Knowles for helpful comments. We are grateful to the Taida Institute for Mathematical\r\nSciences and National Taiwan Universality for their hospitality during part of this\r\nresearch. We thank Thomas Spencer and the Institute for Advanced Study for their\r\nhospitality during the academic year 2013–2014. " article_processing_charge: No arxiv: 1 author: - first_name: Jioon full_name: Lee, Jioon last_name: Lee - first_name: Kevin full_name: Schnelli, Kevin id: 434AD0AE-F248-11E8-B48F-1D18A9856A87 last_name: Schnelli orcid: 0000-0003-0954-3231 - first_name: Ben full_name: Stetler, Ben last_name: Stetler - first_name: Horngtzer full_name: Yau, Horngtzer last_name: Yau citation: ama: Lee J, Schnelli K, Stetler B, Yau H. Bulk universality for deformed wigner matrices. Annals of Probability. 2016;44(3):2349-2425. doi:10.1214/15-AOP1023 apa: Lee, J., Schnelli, K., Stetler, B., & Yau, H. (2016). Bulk universality for deformed wigner matrices. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/15-AOP1023 chicago: Lee, Jioon, Kevin Schnelli, Ben Stetler, and Horngtzer Yau. “Bulk Universality for Deformed Wigner Matrices.” Annals of Probability. Institute of Mathematical Statistics, 2016. https://doi.org/10.1214/15-AOP1023. ieee: J. Lee, K. Schnelli, B. Stetler, and H. Yau, “Bulk universality for deformed wigner matrices,” Annals of Probability, vol. 44, no. 3. Institute of Mathematical Statistics, pp. 2349–2425, 2016. ista: Lee J, Schnelli K, Stetler B, Yau H. 2016. Bulk universality for deformed wigner matrices. Annals of Probability. 44(3), 2349–2425. mla: Lee, Jioon, et al. “Bulk Universality for Deformed Wigner Matrices.” Annals of Probability, vol. 44, no. 3, Institute of Mathematical Statistics, 2016, pp. 2349–425, doi:10.1214/15-AOP1023. short: J. Lee, K. Schnelli, B. Stetler, H. Yau, Annals of Probability 44 (2016) 2349–2425. date_created: 2018-12-11T11:50:47Z date_published: 2016-01-01T00:00:00Z date_updated: 2025-09-22T09:33:43Z day: '01' department: - _id: LaEr doi: 10.1214/15-AOP1023 ec_funded: 1 external_id: arxiv: - '1405.6634' isi: - '000376180700016' intvolume: ' 44' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1405.6634 month: '01' oa: 1 oa_version: Preprint page: 2349 - 2425 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Annals of Probability publication_status: published publisher: Institute of Mathematical Statistics publist_id: '6115' quality_controlled: '1' scopus_import: '1' status: public title: Bulk universality for deformed wigner matrices type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 44 year: '2016' ... --- _id: '1223' abstract: - lang: eng text: We consider a random Schrödinger operator on the binary tree with a random potential which is the sum of a random radially symmetric potential, Qr, and a random transversally periodic potential, κQt, with coupling constant κ. Using a new one-dimensional dynamical systems approach combined with Jensen's inequality in hyperbolic space (our key estimate) we obtain a fractional moment estimate proving localization for small and large κ. Together with a previous result we therefore obtain a model with two Anderson transitions, from localization to delocalization and back to localization, when increasing κ. As a by-product we also have a partially new proof of one-dimensional Anderson localization at any disorder. article_processing_charge: No arxiv: 1 author: - first_name: Richard full_name: Froese, Richard last_name: Froese - first_name: Darrick full_name: Lee, Darrick last_name: Lee - first_name: Christian full_name: Sadel, Christian id: 4760E9F8-F248-11E8-B48F-1D18A9856A87 last_name: Sadel orcid: 0000-0001-8255-3968 - first_name: Wolfgang full_name: Spitzer, Wolfgang last_name: Spitzer - first_name: Günter full_name: Stolz, Günter last_name: Stolz citation: ama: Froese R, Lee D, Sadel C, Spitzer W, Stolz G. Localization for transversally periodic random potentials on binary trees. Journal of Spectral Theory. 2016;6(3):557-600. doi:10.4171/JST/132 apa: Froese, R., Lee, D., Sadel, C., Spitzer, W., & Stolz, G. (2016). Localization for transversally periodic random potentials on binary trees. Journal of Spectral Theory. European Mathematical Society. https://doi.org/10.4171/JST/132 chicago: Froese, Richard, Darrick Lee, Christian Sadel, Wolfgang Spitzer, and Günter Stolz. “Localization for Transversally Periodic Random Potentials on Binary Trees.” Journal of Spectral Theory. European Mathematical Society, 2016. https://doi.org/10.4171/JST/132. ieee: R. Froese, D. Lee, C. Sadel, W. Spitzer, and G. Stolz, “Localization for transversally periodic random potentials on binary trees,” Journal of Spectral Theory, vol. 6, no. 3. European Mathematical Society, pp. 557–600, 2016. ista: Froese R, Lee D, Sadel C, Spitzer W, Stolz G. 2016. Localization for transversally periodic random potentials on binary trees. Journal of Spectral Theory. 6(3), 557–600. mla: Froese, Richard, et al. “Localization for Transversally Periodic Random Potentials on Binary Trees.” Journal of Spectral Theory, vol. 6, no. 3, European Mathematical Society, 2016, pp. 557–600, doi:10.4171/JST/132. short: R. Froese, D. Lee, C. Sadel, W. Spitzer, G. Stolz, Journal of Spectral Theory 6 (2016) 557–600. date_created: 2018-12-11T11:50:48Z date_published: 2016-01-01T00:00:00Z date_updated: 2025-09-22T09:32:55Z day: '01' department: - _id: LaEr doi: 10.4171/JST/132 external_id: arxiv: - '1408.3961' isi: - '000388627000004' intvolume: ' 6' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1408.3961 month: '01' oa: 1 oa_version: Preprint page: 557 - 600 publication: Journal of Spectral Theory publication_status: published publisher: European Mathematical Society publist_id: '6112' quality_controlled: '1' scopus_import: '1' status: public title: Localization for transversally periodic random potentials on binary trees type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 6 year: '2016' ... --- _id: '1434' abstract: - lang: eng text: We prove that the system of subordination equations, defining the free additive convolution of two probability measures, is stable away from the edges of the support and blow-up singularities by showing that the recent smoothness condition of Kargin is always satisfied. As an application, we consider the local spectral statistics of the random matrix ensemble A+UBU⁎A+UBU⁎, where U is a Haar distributed random unitary or orthogonal matrix, and A and B are deterministic matrices. In the bulk regime, we prove that the empirical spectral distribution of A+UBU⁎A+UBU⁎ concentrates around the free additive convolution of the spectral distributions of A and B on scales down to N−2/3N−2/3. article_processing_charge: No arxiv: 1 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 - first_name: Kevin full_name: Schnelli, Kevin id: 434AD0AE-F248-11E8-B48F-1D18A9856A87 last_name: Schnelli orcid: 0000-0003-0954-3231 citation: ama: Bao Z, Erdös L, Schnelli K. Local stability of the free additive convolution. Journal of Functional Analysis. 2016;271(3):672-719. doi:10.1016/j.jfa.2016.04.006 apa: Bao, Z., Erdös, L., & Schnelli, K. (2016). Local stability of the free additive convolution. Journal of Functional Analysis. Academic Press. https://doi.org/10.1016/j.jfa.2016.04.006 chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Stability of the Free Additive Convolution.” Journal of Functional Analysis. Academic Press, 2016. https://doi.org/10.1016/j.jfa.2016.04.006. ieee: Z. Bao, L. Erdös, and K. Schnelli, “Local stability of the free additive convolution,” Journal of Functional Analysis, vol. 271, no. 3. Academic Press, pp. 672–719, 2016. ista: Bao Z, Erdös L, Schnelli K. 2016. Local stability of the free additive convolution. Journal of Functional Analysis. 271(3), 672–719. mla: Bao, Zhigang, et al. “Local Stability of the Free Additive Convolution.” Journal of Functional Analysis, vol. 271, no. 3, Academic Press, 2016, pp. 672–719, doi:10.1016/j.jfa.2016.04.006. short: Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 271 (2016) 672–719. corr_author: '1' date_created: 2018-12-11T11:52:00Z date_published: 2016-08-01T00:00:00Z date_updated: 2025-09-18T14:00:03Z day: '01' department: - _id: LaEr doi: 10.1016/j.jfa.2016.04.006 ec_funded: 1 external_id: arxiv: - '1508.05905' isi: - '000378013400009' intvolume: ' 271' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1508.05905 month: '08' oa: 1 oa_version: Preprint page: 672 - 719 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Journal of Functional Analysis publication_status: published publisher: Academic Press publist_id: '5764' quality_controlled: '1' scopus_import: '1' status: public title: Local stability of the free additive convolution type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 271 year: '2016' ... --- _id: '1257' abstract: - lang: eng text: We consider products of random matrices that are small, independent identically distributed perturbations of a fixed matrix (Formula presented.). Focusing on the eigenvalues of (Formula presented.) of a particular size we obtain a limit to a SDE in a critical scaling. Previous results required (Formula presented.) to be a (conjugated) unitary matrix so it could not have eigenvalues of different modulus. From the result we can also obtain a limit SDE for the Markov process given by the action of the random products on the flag manifold. Applying the result to random Schrödinger operators we can improve some results by Valko and Virag showing GOE statistics for the rescaled eigenvalue process of a sequence of Anderson models on long boxes. In particular, we solve a problem posed in their work. acknowledgement: Open access funding provided by Institute of Science and Technology (IST Austria). The work of C. Sadel was supported by NSERC Discovery Grant 92997-2010 RGPIN and by the People Programme (Marie Curie Actions) of the EU 7th Framework Programme FP7/2007-2013, REA Grant 291734. article_processing_charge: Yes (via OA deal) author: - first_name: Christian full_name: Sadel, Christian id: 4760E9F8-F248-11E8-B48F-1D18A9856A87 last_name: Sadel orcid: 0000-0001-8255-3968 - first_name: Bálint full_name: Virág, Bálint last_name: Virág citation: ama: Sadel C, Virág B. A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes. Communications in Mathematical Physics. 2016;343(3):881-919. doi:10.1007/s00220-016-2600-4 apa: Sadel, C., & Virág, B. (2016). A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-016-2600-4 chicago: Sadel, Christian, and Bálint Virág. “A Central Limit Theorem for Products of Random Matrices and GOE Statistics for the Anderson Model on Long Boxes.” Communications in Mathematical Physics. Springer, 2016. https://doi.org/10.1007/s00220-016-2600-4. ieee: C. Sadel and B. Virág, “A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes,” Communications in Mathematical Physics, vol. 343, no. 3. Springer, pp. 881–919, 2016. ista: Sadel C, Virág B. 2016. A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes. Communications in Mathematical Physics. 343(3), 881–919. mla: Sadel, Christian, and Bálint Virág. “A Central Limit Theorem for Products of Random Matrices and GOE Statistics for the Anderson Model on Long Boxes.” Communications in Mathematical Physics, vol. 343, no. 3, Springer, 2016, pp. 881–919, doi:10.1007/s00220-016-2600-4. short: C. Sadel, B. Virág, Communications in Mathematical Physics 343 (2016) 881–919. corr_author: '1' date_created: 2018-12-11T11:50:59Z date_published: 2016-05-01T00:00:00Z date_updated: 2025-09-22T09:02:32Z day: '01' ddc: - '510' - '539' department: - _id: LaEr doi: 10.1007/s00220-016-2600-4 ec_funded: 1 external_id: isi: - '000374659800005' file: - access_level: open_access checksum: 4fb2411d9c2f56676123165aad46c828 content_type: application/pdf creator: system date_created: 2018-12-12T10:15:02Z date_updated: 2020-07-14T12:44:42Z file_id: '5119' file_name: IST-2016-703-v1+1_s00220-016-2600-4.pdf file_size: 800792 relation: main_file file_date_updated: 2020-07-14T12:44:42Z has_accepted_license: '1' intvolume: ' 343' isi: 1 issue: '3' language: - iso: eng month: '05' oa: 1 oa_version: Published Version page: 881 - 919 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Communications in Mathematical Physics publication_status: published publisher: Springer publist_id: '6067' pubrep_id: '703' quality_controlled: '1' scopus_import: '1' status: public title: A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 343 year: '2016' ... --- _id: '1280' abstract: - lang: eng text: We prove the Wigner-Dyson-Mehta conjecture at fixed energy in the bulk of the spectrum for generalized symmetric and Hermitian Wigner matrices. Previous results concerning the universality of random matrices either require an averaging in the energy parameter or they hold only for Hermitian matrices if the energy parameter is fixed. We develop a homogenization theory of the Dyson Brownian motion and show that microscopic universality follows from mesoscopic statistics. acknowledgement: "The work of P.B. was partially supported by National Sci-\r\nence Foundation Grant DMS-1208859. The work of L.E. was partially supported\r\nby ERC Advanced Grant RANMAT 338804. The work of H.-T. Y. was partially\r\nsupported by National Science Foundation Grant DMS-1307444 and a Simons In-\r\nvestigator award. \ The work of J.Y. was partially supported by National Science\r\nFoundation Grant DMS-1207961. The major part of this research was conducted\r\nwhen all authors were visiting IAS and were also supported by National Science\r\nFoundation Grant DMS-1128255." article_processing_charge: No arxiv: 1 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: Horngtzer full_name: Yau, Horngtzer last_name: Yau - first_name: Jun full_name: Yin, Jun last_name: Yin citation: ama: Bourgade P, Erdös L, Yau H, Yin J. Fixed energy universality for generalized wigner matrices. Communications on Pure and Applied Mathematics. 2016;69(10):1815-1881. doi:10.1002/cpa.21624 apa: Bourgade, P., Erdös, L., Yau, H., & Yin, J. (2016). Fixed energy universality for generalized wigner matrices. Communications on Pure and Applied Mathematics. Wiley-Blackwell. https://doi.org/10.1002/cpa.21624 chicago: Bourgade, Paul, László Erdös, Horngtzer Yau, and Jun Yin. “Fixed Energy Universality for Generalized Wigner Matrices.” Communications on Pure and Applied Mathematics. Wiley-Blackwell, 2016. https://doi.org/10.1002/cpa.21624. ieee: P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Fixed energy universality for generalized wigner matrices,” Communications on Pure and Applied Mathematics, vol. 69, no. 10. Wiley-Blackwell, pp. 1815–1881, 2016. ista: Bourgade P, Erdös L, Yau H, Yin J. 2016. Fixed energy universality for generalized wigner matrices. Communications on Pure and Applied Mathematics. 69(10), 1815–1881. mla: Bourgade, Paul, et al. “Fixed Energy Universality for Generalized Wigner Matrices.” Communications on Pure and Applied Mathematics, vol. 69, no. 10, Wiley-Blackwell, 2016, pp. 1815–81, doi:10.1002/cpa.21624. short: P. Bourgade, L. Erdös, H. Yau, J. Yin, Communications on Pure and Applied Mathematics 69 (2016) 1815–1881. corr_author: '1' date_created: 2018-12-11T11:51:07Z date_published: 2016-10-01T00:00:00Z date_updated: 2025-09-22T08:35:52Z day: '01' department: - _id: LaEr doi: 10.1002/cpa.21624 ec_funded: 1 external_id: arxiv: - '1407.5606' isi: - '000382932900001' intvolume: ' 69' isi: 1 issue: '10' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1407.5606 month: '10' oa: 1 oa_version: Preprint page: 1815 - 1881 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_status: published publisher: Wiley-Blackwell publist_id: '6036' scopus_import: '1' status: public title: Fixed energy universality for generalized wigner matrices type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 69 year: '2016' ... --- _id: '1881' abstract: - lang: eng text: 'We consider random matrices of the form H=W+λV, λ∈ℝ+, where W is a real symmetric or complex Hermitian Wigner matrix of size N and V is a real bounded diagonal random matrix of size N with i.i.d.\ entries that are independent of W. We assume subexponential decay for the matrix entries of W and we choose λ∼1, so that the eigenvalues of W and λV are typically of the same order. Further, we assume that the density of the entries of V is supported on a single interval and is convex near the edges of its support. In this paper we prove that there is λ+∈ℝ+ such that the largest eigenvalues of H are in the limit of large N determined by the order statistics of V for λ>λ+. In particular, the largest eigenvalue of H has a Weibull distribution in the limit N→∞ if λ>λ+. Moreover, for N sufficiently large, we show that the eigenvectors associated to the largest eigenvalues are partially localized for λ>λ+, while they are completely delocalized for λ<λ+. Similar results hold for the lowest eigenvalues. ' acknowledgement: "Most of the presented work was obtained while Kevin Schnelli was staying at the IAS with the support of\r\nThe Fund For Math." article_processing_charge: No arxiv: 1 author: - first_name: Jioon full_name: Lee, Jioon 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. Extremal eigenvalues and eigenvectors of deformed Wigner matrices. Probability Theory and Related Fields. 2016;164(1-2):165-241. doi:10.1007/s00440-014-0610-8 apa: Lee, J., & Schnelli, K. (2016). Extremal eigenvalues and eigenvectors of deformed Wigner matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-014-0610-8 chicago: Lee, Jioon, and Kevin Schnelli. “Extremal Eigenvalues and Eigenvectors of Deformed Wigner Matrices.” Probability Theory and Related Fields. Springer, 2016. https://doi.org/10.1007/s00440-014-0610-8. ieee: J. Lee and K. Schnelli, “Extremal eigenvalues and eigenvectors of deformed Wigner matrices,” Probability Theory and Related Fields, vol. 164, no. 1–2. Springer, pp. 165–241, 2016. ista: Lee J, Schnelli K. 2016. Extremal eigenvalues and eigenvectors of deformed Wigner matrices. Probability Theory and Related Fields. 164(1–2), 165–241. mla: Lee, Jioon, and Kevin Schnelli. “Extremal Eigenvalues and Eigenvectors of Deformed Wigner Matrices.” Probability Theory and Related Fields, vol. 164, no. 1–2, Springer, 2016, pp. 165–241, doi:10.1007/s00440-014-0610-8. short: J. Lee, K. Schnelli, Probability Theory and Related Fields 164 (2016) 165–241. corr_author: '1' date_created: 2018-12-11T11:54:31Z date_published: 2016-02-01T00:00:00Z date_updated: 2025-09-18T10:46:46Z day: '01' department: - _id: LaEr doi: 10.1007/s00440-014-0610-8 ec_funded: 1 external_id: arxiv: - '1310.7057' isi: - '000373163300006' intvolume: ' 164' isi: 1 issue: 1-2 language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1310.7057 month: '02' oa: 1 oa_version: Preprint page: 165 - 241 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: '5215' quality_controlled: '1' scopus_import: '1' status: public title: Extremal eigenvalues and eigenvectors of deformed Wigner matrices type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 164 year: '2016' ... --- _id: '1489' abstract: - lang: eng text: 'We prove optimal local law, bulk universality and non-trivial decay for the off-diagonal elements of the resolvent for a class of translation invariant Gaussian random matrix ensembles with correlated entries. ' acknowledgement: Open access funding provided by Institute of Science and Technology (IST Austria). Oskari H. Ajanki was Partially supported by ERC Advanced Grant RANMAT No. 338804, and SFB-TR 12 Grant of the German Research Council. László Erdős was Partially supported by ERC Advanced Grant RANMAT No. 338804. Torben Krüger was Partially supported by ERC Advanced Grant RANMAT No. 338804, and SFB-TR 12 Grant of the German Research Council. article_processing_charge: Yes (via OA deal) author: - first_name: Oskari H full_name: Ajanki, Oskari H id: 36F2FB7E-F248-11E8-B48F-1D18A9856A87 last_name: Ajanki - 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: Ajanki OH, Erdös L, Krüger TH. Local spectral statistics of Gaussian matrices with correlated entries. Journal of Statistical Physics. 2016;163(2):280-302. doi:10.1007/s10955-016-1479-y apa: Ajanki, O. H., Erdös, L., & Krüger, T. H. (2016). Local spectral statistics of Gaussian matrices with correlated entries. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-016-1479-y chicago: Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Local Spectral Statistics of Gaussian Matrices with Correlated Entries.” Journal of Statistical Physics. Springer, 2016. https://doi.org/10.1007/s10955-016-1479-y. ieee: O. H. Ajanki, L. Erdös, and T. H. Krüger, “Local spectral statistics of Gaussian matrices with correlated entries,” Journal of Statistical Physics, vol. 163, no. 2. Springer, pp. 280–302, 2016. ista: Ajanki OH, Erdös L, Krüger TH. 2016. Local spectral statistics of Gaussian matrices with correlated entries. Journal of Statistical Physics. 163(2), 280–302. mla: Ajanki, Oskari H., et al. “Local Spectral Statistics of Gaussian Matrices with Correlated Entries.” Journal of Statistical Physics, vol. 163, no. 2, Springer, 2016, pp. 280–302, doi:10.1007/s10955-016-1479-y. short: O.H. Ajanki, L. Erdös, T.H. Krüger, Journal of Statistical Physics 163 (2016) 280–302. corr_author: '1' date_created: 2018-12-11T11:52:19Z date_published: 2016-04-01T00:00:00Z date_updated: 2025-09-18T11:17:50Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1007/s10955-016-1479-y ec_funded: 1 external_id: isi: - '000373132700003' file: - access_level: open_access checksum: 7139598dcb1cafbe6866bd2bfd732b33 content_type: application/pdf creator: system date_created: 2018-12-12T10:11:16Z date_updated: 2020-07-14T12:44:57Z file_id: '4869' file_name: IST-2016-516-v1+1_s10955-016-1479-y.pdf file_size: 660602 relation: main_file file_date_updated: 2020-07-14T12:44:57Z has_accepted_license: '1' intvolume: ' 163' isi: 1 issue: '2' language: - iso: eng month: '04' oa: 1 oa_version: Published Version page: 280 - 302 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Journal of Statistical Physics publication_status: published publisher: Springer publist_id: '5698' pubrep_id: '516' quality_controlled: '1' scopus_import: '1' status: public title: Local spectral statistics of Gaussian matrices with correlated entries 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 163 year: '2016' ... --- _id: '1608' abstract: - lang: eng text: 'We show that the Anderson model has a transition from localization to delocalization at exactly 2 dimensional growth rate on antitrees with normalized edge weights which are certain discrete graphs. The kinetic part has a one-dimensional structure allowing a description through transfer matrices which involve some Schur complement. For such operators we introduce the notion of having one propagating channel and extend theorems from the theory of one-dimensional Jacobi operators that relate the behavior of transfer matrices with the spectrum. These theorems are then applied to the considered model. In essence, in a certain energy region the kinetic part averages the random potentials along shells and the transfer matrices behave similar as for a one-dimensional operator with random potential of decaying variance. At d dimensional growth for d>2 this effective decay is strong enough to obtain absolutely continuous spectrum, whereas for some uniform d dimensional growth with d<2 one has pure point spectrum in this energy region. At exactly uniform 2 dimensional growth also some singular continuous spectrum appears, at least at small disorder. As a corollary we also obtain a change from singular spectrum (d≤2) to absolutely continuous spectrum (d≥3) for random operators of the type rΔdr+λ on ℤd, where r is an orthogonal radial projection, Δd the discrete adjacency operator (Laplacian) on ℤd and λ a random potential. ' article_processing_charge: No arxiv: 1 author: - first_name: Christian full_name: Sadel, Christian id: 4760E9F8-F248-11E8-B48F-1D18A9856A87 last_name: Sadel orcid: 0000-0001-8255-3968 citation: ama: Sadel C. Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel. Annales Henri Poincare. 2016;17(7):1631-1675. doi:10.1007/s00023-015-0456-3 apa: Sadel, C. (2016). Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel. Annales Henri Poincare. Birkhäuser. https://doi.org/10.1007/s00023-015-0456-3 chicago: Sadel, Christian. “Anderson Transition at 2 Dimensional Growth Rate on Antitrees and Spectral Theory for Operators with One Propagating Channel.” Annales Henri Poincare. Birkhäuser, 2016. https://doi.org/10.1007/s00023-015-0456-3. ieee: C. Sadel, “Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel,” Annales Henri Poincare, vol. 17, no. 7. Birkhäuser, pp. 1631–1675, 2016. ista: Sadel C. 2016. Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel. Annales Henri Poincare. 17(7), 1631–1675. mla: Sadel, Christian. “Anderson Transition at 2 Dimensional Growth Rate on Antitrees and Spectral Theory for Operators with One Propagating Channel.” Annales Henri Poincare, vol. 17, no. 7, Birkhäuser, 2016, pp. 1631–75, doi:10.1007/s00023-015-0456-3. short: C. Sadel, Annales Henri Poincare 17 (2016) 1631–1675. corr_author: '1' date_created: 2018-12-11T11:53:00Z date_published: 2016-07-01T00:00:00Z date_updated: 2025-09-18T11:00:43Z day: '01' department: - _id: LaEr doi: 10.1007/s00023-015-0456-3 ec_funded: 1 external_id: arxiv: - '1501.04287' isi: - '000377994000003' intvolume: ' 17' isi: 1 issue: '7' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1501.04287 month: '07' oa: 1 oa_version: Preprint page: 1631 - 1675 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Annales Henri Poincare publication_status: published publisher: Birkhäuser publist_id: '5558' quality_controlled: '1' scopus_import: '1' status: public title: Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel type: journal_article user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 17 year: '2016' ... --- _id: '1824' abstract: - lang: eng text: Condensation phenomena arise through a collective behaviour of particles. They are observed in both classical and quantum systems, ranging from the formation of traffic jams in mass transport models to the macroscopic occupation of the energetic ground state in ultra-cold bosonic gases (Bose-Einstein condensation). Recently, it has been shown that a driven and dissipative system of bosons may form multiple condensates. Which states become the condensates has, however, remained elusive thus far. The dynamics of this condensation are described by coupled birth-death processes, which also occur in evolutionary game theory. Here we apply concepts from evolutionary game theory to explain the formation of multiple condensates in such driven-dissipative bosonic systems. We show that the vanishing of relative entropy production determines their selection. The condensation proceeds exponentially fast, but the system never comes to rest. Instead, the occupation numbers of condensates may oscillate, as we demonstrate for a rock-paper-scissors game of condensates. article_number: '6977' article_processing_charge: No author: - first_name: Johannes full_name: Knebel, Johannes last_name: Knebel - first_name: Markus full_name: Weber, Markus last_name: Weber - 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: Erwin full_name: Frey, Erwin last_name: Frey citation: ama: Knebel J, Weber M, Krüger TH, Frey E. Evolutionary games of condensates in coupled birth-death processes. Nature Communications. 2015;6. doi:10.1038/ncomms7977 apa: Knebel, J., Weber, M., Krüger, T. H., & Frey, E. (2015). Evolutionary games of condensates in coupled birth-death processes. Nature Communications. Nature Publishing Group. https://doi.org/10.1038/ncomms7977 chicago: Knebel, Johannes, Markus Weber, Torben H Krüger, and Erwin Frey. “Evolutionary Games of Condensates in Coupled Birth-Death Processes.” Nature Communications. Nature Publishing Group, 2015. https://doi.org/10.1038/ncomms7977. ieee: J. Knebel, M. Weber, T. H. Krüger, and E. Frey, “Evolutionary games of condensates in coupled birth-death processes,” Nature Communications, vol. 6. Nature Publishing Group, 2015. ista: Knebel J, Weber M, Krüger TH, Frey E. 2015. Evolutionary games of condensates in coupled birth-death processes. Nature Communications. 6, 6977. mla: Knebel, Johannes, et al. “Evolutionary Games of Condensates in Coupled Birth-Death Processes.” Nature Communications, vol. 6, 6977, Nature Publishing Group, 2015, doi:10.1038/ncomms7977. short: J. Knebel, M. Weber, T.H. Krüger, E. Frey, Nature Communications 6 (2015). date_created: 2018-12-11T11:54:13Z date_published: 2015-04-24T00:00:00Z date_updated: 2025-09-23T08:44:01Z day: '24' ddc: - '530' department: - _id: LaEr doi: 10.1038/ncomms7977 external_id: isi: - '000353705000003' file: - access_level: open_access checksum: c4cffb5c8b245e658a34eac71a03e7cc content_type: application/pdf creator: system date_created: 2018-12-12T10:16:54Z date_updated: 2020-07-14T12:45:17Z file_id: '5245' file_name: IST-2016-451-v1+1_ncomms7977.pdf file_size: 1151501 relation: main_file file_date_updated: 2020-07-14T12:45:17Z has_accepted_license: '1' intvolume: ' 6' isi: 1 language: - iso: eng month: '04' oa: 1 oa_version: Published Version publication: Nature Communications publication_status: published publisher: Nature Publishing Group publist_id: '5282' pubrep_id: '451' quality_controlled: '1' scopus_import: '1' status: public title: Evolutionary games of condensates in coupled birth-death processes 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: 317138e5-6ab7-11ef-aa6d-ffef3953e345 volume: 6 year: '2015' ... --- _id: '1864' abstract: - lang: eng text: "The Altshuler–Shklovskii formulas (Altshuler and Shklovskii, BZh Eksp Teor Fiz 91:200, 1986) predict, for any disordered quantum system in the diffusive regime, a universal power law behaviour for the correlation functions of the mesoscopic eigenvalue density. In this paper and its companion (Erdős and Knowles, The Altshuler–Shklovskii formulas for random band matrices I: the unimodular case, 2013), we prove these formulas for random band matrices. In (Erdős and Knowles, The Altshuler–Shklovskii formulas for random band matrices I: the unimodular case, 2013) we introduced a diagrammatic approach and presented robust estimates on general diagrams under certain simplifying assumptions. In this paper, we remove these assumptions by giving a general estimate of the subleading diagrams. We also give a precise analysis of the leading diagrams which give rise to the Altschuler–Shklovskii power laws. Moreover, we introduce a family of general random band matrices which interpolates between real symmetric (β = 1) and complex Hermitian (β = 2) models, and track the transition for the mesoscopic density–density correlation. Finally, we address the higher-order correlation functions by proving that they behave asymptotically according to a Gaussian process whose covariance is given by the Altshuler–Shklovskii formulas.\r\n" article_processing_charge: No arxiv: 1 author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Antti full_name: Knowles, Antti last_name: Knowles citation: ama: 'Erdös L, Knowles A. The Altshuler-Shklovskii formulas for random band matrices II: The general case. Annales Henri Poincare. 2015;16(3):709-799. doi:10.1007/s00023-014-0333-5' apa: 'Erdös, L., & Knowles, A. (2015). The Altshuler-Shklovskii formulas for random band matrices II: The general case. Annales Henri Poincare. Springer. https://doi.org/10.1007/s00023-014-0333-5' chicago: 'Erdös, László, and Antti Knowles. “The Altshuler-Shklovskii Formulas for Random Band Matrices II: The General Case.” Annales Henri Poincare. Springer, 2015. https://doi.org/10.1007/s00023-014-0333-5.' ieee: 'L. Erdös and A. Knowles, “The Altshuler-Shklovskii formulas for random band matrices II: The general case,” Annales Henri Poincare, vol. 16, no. 3. Springer, pp. 709–799, 2015.' ista: 'Erdös L, Knowles A. 2015. The Altshuler-Shklovskii formulas for random band matrices II: The general case. Annales Henri Poincare. 16(3), 709–799.' mla: 'Erdös, László, and Antti Knowles. “The Altshuler-Shklovskii Formulas for Random Band Matrices II: The General Case.” Annales Henri Poincare, vol. 16, no. 3, Springer, 2015, pp. 709–99, doi:10.1007/s00023-014-0333-5.' short: L. Erdös, A. Knowles, Annales Henri Poincare 16 (2015) 709–799. date_created: 2018-12-11T11:54:26Z date_published: 2015-03-01T00:00:00Z date_updated: 2025-10-22T10:23:38Z day: '01' department: - _id: LaEr doi: 10.1007/s00023-014-0333-5 ec_funded: 1 external_id: arxiv: - '1309.5107' isi: - '000349364100002' intvolume: ' 16' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1309.5107 month: '03' oa: 1 oa_version: Preprint page: 709 - 799 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Annales Henri Poincare publication_status: published publisher: Springer publist_id: '5233' scopus_import: '1' status: public title: 'The Altshuler-Shklovskii formulas for random band matrices II: The general case' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 16 year: '2015' ...