--- _id: '7618' abstract: - lang: eng text: 'This short note aims to study quantum Hellinger distances investigated recently by Bhatia et al. (Lett Math Phys 109:1777–1804, 2019) with a particular emphasis on barycenters. We introduce the family of generalized quantum Hellinger divergences that are of the form ϕ(A,B)=Tr((1−c)A+cB−AσB), where σ is an arbitrary Kubo–Ando mean, and c∈(0,1) is the weight of σ. We note that these divergences belong to the family of maximal quantum f-divergences, and hence are jointly convex, and satisfy the data processing inequality. We derive a characterization of the barycenter of finitely many positive definite operators for these generalized quantum Hellinger divergences. We note that the characterization of the barycenter as the weighted multivariate 1/2-power mean, that was claimed in Bhatia et al. (2019), is true in the case of commuting operators, but it is not correct in the general case. ' acknowledgement: "J. Pitrik was supported by the Hungarian Academy of Sciences Lendület-Momentum Grant for Quantum\r\nInformation Theory, No. 96 141, and by the Hungarian National Research, Development and Innovation\r\nOffice (NKFIH) via Grants Nos. K119442, K124152 and KH129601. D. Virosztek was supported by the\r\nISTFELLOW program of the Institute of Science and Technology Austria (Project Code IC1027FELL01),\r\nby the European Union’s Horizon 2020 research and innovation program under the Marie\r\nSklodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National\r\nResearch, Development and Innovation Office (NKFIH) via Grants Nos. K124152 and KH129601.\r\nWe are grateful to Milán Mosonyi for drawing our attention to Ref.’s [6,14,15,17,\r\n20,21], for comments on earlier versions of this paper, and for several discussions on the topic. We are\r\nalso grateful to Miklós Pálfia for several discussions; to László Erdös for his essential suggestions on the\r\nstructure and highlights of this paper, and for his comments on earlier versions; and to the anonymous\r\nreferee for his/her valuable comments and suggestions." article_processing_charge: No article_type: original author: - first_name: Jozsef full_name: Pitrik, Jozsef last_name: Pitrik - first_name: Daniel full_name: Virosztek, Daniel id: 48DB45DA-F248-11E8-B48F-1D18A9856A87 last_name: Virosztek orcid: 0000-0003-1109-5511 citation: ama: Pitrik J, Virosztek D. Quantum Hellinger distances revisited. Letters in Mathematical Physics. 2020;110(8):2039-2052. doi:10.1007/s11005-020-01282-0 apa: Pitrik, J., & Virosztek, D. (2020). Quantum Hellinger distances revisited. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-020-01282-0 chicago: Pitrik, Jozsef, and Daniel Virosztek. “Quantum Hellinger Distances Revisited.” Letters in Mathematical Physics. Springer Nature, 2020. https://doi.org/10.1007/s11005-020-01282-0. ieee: J. Pitrik and D. Virosztek, “Quantum Hellinger distances revisited,” Letters in Mathematical Physics, vol. 110, no. 8. Springer Nature, pp. 2039–2052, 2020. ista: Pitrik J, Virosztek D. 2020. Quantum Hellinger distances revisited. Letters in Mathematical Physics. 110(8), 2039–2052. mla: Pitrik, Jozsef, and Daniel Virosztek. “Quantum Hellinger Distances Revisited.” Letters in Mathematical Physics, vol. 110, no. 8, Springer Nature, 2020, pp. 2039–52, doi:10.1007/s11005-020-01282-0. short: J. Pitrik, D. Virosztek, Letters in Mathematical Physics 110 (2020) 2039–2052. date_created: 2020-03-25T15:57:48Z date_published: 2020-08-01T00:00:00Z date_updated: 2023-08-18T10:17:26Z day: '01' department: - _id: LaEr doi: 10.1007/s11005-020-01282-0 ec_funded: 1 external_id: arxiv: - '1903.10455' isi: - '000551556000002' intvolume: ' 110' isi: 1 issue: '8' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1903.10455 month: '08' oa: 1 oa_version: Preprint page: 2039-2052 project: - _id: 26A455A6-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '846294' name: Geometric study of Wasserstein spaces and free probability - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Letters in Mathematical Physics publication_identifier: eissn: - 1573-0530 issn: - 0377-9017 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Quantum Hellinger distances revisited type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 110 year: '2020' ... --- _id: '9104' abstract: - lang: eng text: We consider the free additive convolution of two probability measures μ and ν on the real line and show that μ ⊞ v is supported on a single interval if μ and ν each has single interval support. Moreover, the density of μ ⊞ ν is proven to vanish as a square root near the edges of its support if both μ and ν have power law behavior with exponents between −1 and 1 near their edges. In particular, these results show the ubiquity of the conditions in our recent work on optimal local law at the spectral edges for addition of random matrices [5]. acknowledgement: "Supported in part by Hong Kong RGC Grant ECS 26301517.\r\nSupported in part by ERC Advanced Grant RANMAT No. 338804.\r\nSupported in part by the Knut and Alice Wallenberg Foundation and the Swedish Research Council Grant VR-2017-05195." article_processing_charge: No 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 - 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. On the support of the free additive convolution. Journal d’Analyse Mathematique. 2020;142:323-348. doi:10.1007/s11854-020-0135-2 apa: Bao, Z., Erdös, L., & Schnelli, K. (2020). On the support of the free additive convolution. Journal d’Analyse Mathematique. Springer Nature. https://doi.org/10.1007/s11854-020-0135-2 chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “On the Support of the Free Additive Convolution.” Journal d’Analyse Mathematique. Springer Nature, 2020. https://doi.org/10.1007/s11854-020-0135-2. ieee: Z. Bao, L. Erdös, and K. Schnelli, “On the support of the free additive convolution,” Journal d’Analyse Mathematique, vol. 142. Springer Nature, pp. 323–348, 2020. ista: Bao Z, Erdös L, Schnelli K. 2020. On the support of the free additive convolution. Journal d’Analyse Mathematique. 142, 323–348. mla: Bao, Zhigang, et al. “On the Support of the Free Additive Convolution.” Journal d’Analyse Mathematique, vol. 142, Springer Nature, 2020, pp. 323–48, doi:10.1007/s11854-020-0135-2. short: Z. Bao, L. Erdös, K. Schnelli, Journal d’Analyse Mathematique 142 (2020) 323–348. date_created: 2021-02-07T23:01:15Z date_published: 2020-11-01T00:00:00Z date_updated: 2023-08-24T11:16:03Z day: '01' department: - _id: LaEr doi: 10.1007/s11854-020-0135-2 ec_funded: 1 external_id: arxiv: - '1804.11199' isi: - '000611879400008' intvolume: ' 142' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1804.11199 month: '11' oa: 1 oa_version: Preprint page: 323-348 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Journal d'Analyse Mathematique publication_identifier: eissn: - '15658538' issn: - '00217670' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: On the support of the free additive convolution type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 142 year: '2020' ... --- _id: '10862' abstract: - lang: eng text: We consider the sum of two large Hermitian matrices A and B with a Haar unitary conjugation bringing them into a general relative position. We prove that the eigenvalue density on the scale slightly above the local eigenvalue spacing is asymptotically given by the free additive convolution of the laws of A and B as the dimension of the matrix increases. This implies optimal rigidity of the eigenvalues and optimal rate of convergence in Voiculescu's theorem. Our previous works [4], [5] established these results in the bulk spectrum, the current paper completely settles the problem at the spectral edges provided they have the typical square-root behavior. The key element of our proof is to compensate the deterioration of the stability of the subordination equations by sharp error estimates that properly account for the local density near the edge. Our results also hold if the Haar unitary matrix is replaced by the Haar orthogonal matrix. acknowledgement: Partially supported by ERC Advanced Grant RANMAT No. 338804. article_number: '108639' article_processing_charge: No 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 - first_name: Kevin full_name: Schnelli, Kevin last_name: Schnelli citation: ama: Bao Z, Erdös L, Schnelli K. Spectral rigidity for addition of random matrices at the regular edge. Journal of Functional Analysis. 2020;279(7). doi:10.1016/j.jfa.2020.108639 apa: Bao, Z., Erdös, L., & Schnelli, K. (2020). Spectral rigidity for addition of random matrices at the regular edge. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2020.108639 chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” Journal of Functional Analysis. Elsevier, 2020. https://doi.org/10.1016/j.jfa.2020.108639. ieee: Z. Bao, L. Erdös, and K. Schnelli, “Spectral rigidity for addition of random matrices at the regular edge,” Journal of Functional Analysis, vol. 279, no. 7. Elsevier, 2020. ista: Bao Z, Erdös L, Schnelli K. 2020. Spectral rigidity for addition of random matrices at the regular edge. Journal of Functional Analysis. 279(7), 108639. mla: Bao, Zhigang, et al. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” Journal of Functional Analysis, vol. 279, no. 7, 108639, Elsevier, 2020, doi:10.1016/j.jfa.2020.108639. short: Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 279 (2020). date_created: 2022-03-18T10:18:59Z date_published: 2020-10-15T00:00:00Z date_updated: 2023-08-24T14:08:42Z day: '15' department: - _id: LaEr doi: 10.1016/j.jfa.2020.108639 ec_funded: 1 external_id: arxiv: - '1708.01597' isi: - '000559623200009' intvolume: ' 279' isi: 1 issue: '7' keyword: - Analysis language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1708.01597 month: '10' 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: Journal of Functional Analysis publication_identifier: issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Spectral rigidity for addition of random matrices at the regular edge type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 279 year: '2020' ... --- _id: '6488' abstract: - lang: eng text: We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix W˜ and its minor W. We find that the fluctuation of this difference is much smaller than those of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of W˜ and W. Our result identifies the fluctuation of the spatial derivative of the approximate Gaussian field in the recent paper by Dumitru and Paquette. Unlike in a similar result for Wigner matrices, for sample covariance matrices, the fluctuation may entirely vanish. article_number: '2050006' article_processing_charge: No article_type: original author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 citation: ama: 'Cipolloni G, Erdös L. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. 2020;9(3). doi:10.1142/S2010326320500069' apa: 'Cipolloni, G., & Erdös, L. (2020). Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. World Scientific Publishing. https://doi.org/10.1142/S2010326320500069' chicago: 'Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices: Theory and Application. World Scientific Publishing, 2020. https://doi.org/10.1142/S2010326320500069.' ieee: 'G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices,” Random Matrices: Theory and Application, vol. 9, no. 3. World Scientific Publishing, 2020.' ista: 'Cipolloni G, Erdös L. 2020. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. 9(3), 2050006.' mla: 'Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices: Theory and Application, vol. 9, no. 3, 2050006, World Scientific Publishing, 2020, doi:10.1142/S2010326320500069.' short: 'G. Cipolloni, L. Erdös, Random Matrices: Theory and Application 9 (2020).' date_created: 2019-05-26T21:59:14Z date_published: 2020-07-01T00:00:00Z date_updated: 2023-08-28T08:38:48Z day: '01' department: - _id: LaEr doi: 10.1142/S2010326320500069 ec_funded: 1 external_id: arxiv: - '1806.08751' isi: - '000547464400001' intvolume: ' 9' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1806.08751 month: '07' 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 - _id: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program publication: 'Random Matrices: Theory and Application' publication_identifier: eissn: - '20103271' issn: - '20103263' publication_status: published publisher: World Scientific Publishing quality_controlled: '1' scopus_import: '1' status: public title: Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 9 year: '2020' ... --- _id: '6185' abstract: - lang: eng text: For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are universal 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 in the complex Hermitian class. Our analysis holds not only for exact cusps, but approximate cusps as well, where an extended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp for both symmetry classes. This result is also the key input in the companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where the cusp universality for real symmetric Wigner-type matrices is proven. The novel cusp fluctuation mechanism is also essential for the recent results on the spectral radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian edge universality (Cipolloni et al. in Edge universality for non-Hermitian random matrices, 2019. arXiv:1908.00969). acknowledgement: Open access funding provided by Institute of Science and Technology (IST Austria). The authors are very grateful to Johannes Alt for numerous discussions on the Dyson equation and for his invaluable help in adjusting [10] to the needs of the present work. article_processing_charge: Yes (via OA deal) article_type: original 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: 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, Krüger TH, Schröder DJ. Cusp universality for random matrices I: Local law and the complex Hermitian case. Communications in Mathematical Physics. 2020;378:1203-1278. doi:10.1007/s00220-019-03657-4' apa: 'Erdös, L., Krüger, T. H., & Schröder, D. J. (2020). Cusp universality for random matrices I: Local law and the complex Hermitian case. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03657-4' chicago: 'Erdös, László, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” Communications in Mathematical Physics. Springer Nature, 2020. https://doi.org/10.1007/s00220-019-03657-4.' ieee: 'L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices I: Local law and the complex Hermitian case,” Communications in Mathematical Physics, vol. 378. Springer Nature, pp. 1203–1278, 2020.' ista: 'Erdös L, Krüger TH, Schröder DJ. 2020. Cusp universality for random matrices I: Local law and the complex Hermitian case. Communications in Mathematical Physics. 378, 1203–1278.' mla: 'Erdös, László, et al. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” Communications in Mathematical Physics, vol. 378, Springer Nature, 2020, pp. 1203–78, doi:10.1007/s00220-019-03657-4.' short: L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics 378 (2020) 1203–1278. date_created: 2019-03-28T10:21:15Z date_published: 2020-09-01T00:00:00Z date_updated: 2023-09-07T12:54:12Z day: '01' ddc: - '530' - '510' department: - _id: LaEr doi: 10.1007/s00220-019-03657-4 ec_funded: 1 external_id: arxiv: - '1809.03971' isi: - '000529483000001' file: - access_level: open_access checksum: c3a683e2afdcea27afa6880b01e53dc2 content_type: application/pdf creator: dernst date_created: 2020-11-18T11:14:37Z date_updated: 2020-11-18T11:14:37Z file_id: '8771' file_name: 2020_CommMathPhysics_Erdoes.pdf file_size: 2904574 relation: main_file success: 1 file_date_updated: 2020-11-18T11:14:37Z has_accepted_license: '1' intvolume: ' 378' isi: 1 language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: 1203-1278 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: Communications in Mathematical Physics publication_identifier: eissn: - 1432-0916 issn: - 0010-3616 publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: record: - id: '6179' relation: dissertation_contains status: public scopus_import: '1' status: public title: 'Cusp universality for random matrices I: Local law and the complex Hermitian case' 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 378 year: '2020' ... --- _id: '14694' abstract: - lang: eng text: We study the unique solution m of the Dyson equation \( -m(z)^{-1} = z\1 - a + S[m(z)] \) on a von Neumann algebra A with the constraint Imm≥0. Here, z lies in the complex upper half-plane, a is a self-adjoint element of A and S is a positivity-preserving linear operator on A. We show that m is the Stieltjes transform of a compactly supported A-valued measure on R. Under suitable assumptions, we establish that this measure has a uniformly 1/3-Hölder continuous density with respect to the Lebesgue measure, which is supported on finitely many intervals, called bands. In fact, the density is analytic inside the bands with a square-root growth at the edges and internal cubic root cusps whenever the gap between two bands vanishes. The shape of these singularities is universal and no other singularity may occur. We give a precise asymptotic description of m near the singular points. These asymptotics generalize the analysis at the regular edges given in the companion paper on the Tracy-Widom universality for the edge eigenvalue statistics for correlated random matrices [the first author et al., Ann. Probab. 48, No. 2, 963--1001 (2020; Zbl 1434.60017)] and they play a key role in the proof of the Pearcey universality at the cusp for Wigner-type matrices [G. Cipolloni et al., Pure Appl. Anal. 1, No. 4, 615--707 (2019; Zbl 07142203); the second author et al., Commun. Math. Phys. 378, No. 2, 1203--1278 (2020; Zbl 07236118)]. We also extend the finite dimensional band mass formula from [the first author et al., loc. cit.] to the von Neumann algebra setting by showing that the spectral mass of the bands is topologically rigid under deformations and we conclude that these masses are quantized in some important cases. article_processing_charge: Yes 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. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. Documenta Mathematica. 2020;25:1421-1539. doi:10.4171/dm/780' apa: 'Alt, J., Erdös, L., & Krüger, T. H. (2020). The Dyson equation with linear self-energy: Spectral bands, edges and cusps. Documenta Mathematica. EMS Press. https://doi.org/10.4171/dm/780' chicago: 'Alt, Johannes, László Erdös, and Torben H Krüger. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” Documenta Mathematica. EMS Press, 2020. https://doi.org/10.4171/dm/780.' ieee: 'J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy: Spectral bands, edges and cusps,” Documenta Mathematica, vol. 25. EMS Press, pp. 1421–1539, 2020.' ista: 'Alt J, Erdös L, Krüger TH. 2020. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. Documenta Mathematica. 25, 1421–1539.' mla: 'Alt, Johannes, et al. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” Documenta Mathematica, vol. 25, EMS Press, 2020, pp. 1421–539, doi:10.4171/dm/780.' short: J. Alt, L. Erdös, T.H. Krüger, Documenta Mathematica 25 (2020) 1421–1539. date_created: 2023-12-18T10:37:43Z date_published: 2020-09-01T00:00:00Z date_updated: 2023-12-18T10:46:09Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.4171/dm/780 external_id: arxiv: - '1804.07752' file: - access_level: open_access checksum: 12aacc1d63b852ff9a51c1f6b218d4a6 content_type: application/pdf creator: dernst date_created: 2023-12-18T10:42:32Z date_updated: 2023-12-18T10:42:32Z file_id: '14695' file_name: 2020_DocumentaMathematica_Alt.pdf file_size: 1374708 relation: main_file success: 1 file_date_updated: 2023-12-18T10:42:32Z has_accepted_license: '1' intvolume: ' 25' keyword: - General Mathematics language: - iso: eng month: '09' oa: 1 oa_version: Published Version page: 1421-1539 publication: Documenta Mathematica publication_identifier: eissn: - 1431-0643 issn: - 1431-0635 publication_status: published publisher: EMS Press quality_controlled: '1' related_material: record: - id: '6183' relation: earlier_version status: public status: public title: 'The Dyson equation with linear self-energy: Spectral bands, edges and cusps' 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: 25 year: '2020' ... --- _id: '6184' abstract: - lang: eng text: We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal edges of the self-consistent density of states. In particular, we establish a strong form of band rigidity which excludes mismatches between location and label of eigenvalues close to internal edges in these general models. 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 - 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: 'Alt J, Erdös L, Krüger TH, Schröder DJ. Correlated random matrices: Band rigidity and edge universality. Annals of Probability. 2020;48(2):963-1001. doi:10.1214/19-AOP1379' apa: 'Alt, J., Erdös, L., Krüger, T. H., & Schröder, D. J. (2020). Correlated random matrices: Band rigidity and edge universality. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/19-AOP1379' chicago: 'Alt, Johannes, László Erdös, Torben H Krüger, and Dominik J Schröder. “Correlated Random Matrices: Band Rigidity and Edge Universality.” Annals of Probability. Institute of Mathematical Statistics, 2020. https://doi.org/10.1214/19-AOP1379.' ieee: 'J. Alt, L. Erdös, T. H. Krüger, and D. J. Schröder, “Correlated random matrices: Band rigidity and edge universality,” Annals of Probability, vol. 48, no. 2. Institute of Mathematical Statistics, pp. 963–1001, 2020.' ista: 'Alt J, Erdös L, Krüger TH, Schröder DJ. 2020. Correlated random matrices: Band rigidity and edge universality. Annals of Probability. 48(2), 963–1001.' mla: 'Alt, Johannes, et al. “Correlated Random Matrices: Band Rigidity and Edge Universality.” Annals of Probability, vol. 48, no. 2, Institute of Mathematical Statistics, 2020, pp. 963–1001, doi:10.1214/19-AOP1379.' short: J. Alt, L. Erdös, T.H. Krüger, D.J. Schröder, Annals of Probability 48 (2020) 963–1001. date_created: 2019-03-28T09:20:08Z date_published: 2020-03-01T00:00:00Z date_updated: 2024-02-22T14:34:33Z day: '01' department: - _id: LaEr doi: 10.1214/19-AOP1379 ec_funded: 1 external_id: arxiv: - '1804.07744' isi: - '000528269100013' intvolume: ' 48' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1804.07744 month: '03' oa: 1 oa_version: Preprint page: 963-1001 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_identifier: issn: - 0091-1798 publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' related_material: record: - id: '149' relation: dissertation_contains status: public - id: '6179' relation: dissertation_contains status: public scopus_import: '1' status: public title: 'Correlated random matrices: Band rigidity and edge universality' type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 48 year: '2020' ... --- _id: '15063' abstract: - lang: eng text: We consider the least singular value of a large random matrix with real or complex i.i.d. Gaussian entries shifted by a constant z∈C. We prove an optimal lower tail estimate on this singular value in the critical regime where z is around the spectral edge, thus improving the classical bound of Sankar, Spielman and Teng (SIAM J. Matrix Anal. Appl. 28:2 (2006), 446–476) for the particular shift-perturbation in the edge regime. Lacking Brézin–Hikami formulas in the real case, we rely on the superbosonization formula (Comm. Math. Phys. 283:2 (2008), 343–395). acknowledgement: Partially supported by ERC Advanced Grant No. 338804. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 66538 article_processing_charge: No article_type: original author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - 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: Cipolloni G, Erdös L, Schröder DJ. Optimal lower bound on the least singular value of the shifted Ginibre ensemble. Probability and Mathematical Physics. 2020;1(1):101-146. doi:10.2140/pmp.2020.1.101 apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2020). Optimal lower bound on the least singular value of the shifted Ginibre ensemble. Probability and Mathematical Physics. Mathematical Sciences Publishers. https://doi.org/10.2140/pmp.2020.1.101 chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble.” Probability and Mathematical Physics. Mathematical Sciences Publishers, 2020. https://doi.org/10.2140/pmp.2020.1.101. ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal lower bound on the least singular value of the shifted Ginibre ensemble,” Probability and Mathematical Physics, vol. 1, no. 1. Mathematical Sciences Publishers, pp. 101–146, 2020. ista: Cipolloni G, Erdös L, Schröder DJ. 2020. Optimal lower bound on the least singular value of the shifted Ginibre ensemble. Probability and Mathematical Physics. 1(1), 101–146. mla: Cipolloni, Giorgio, et al. “Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble.” Probability and Mathematical Physics, vol. 1, no. 1, Mathematical Sciences Publishers, 2020, pp. 101–46, doi:10.2140/pmp.2020.1.101. short: G. Cipolloni, L. Erdös, D.J. Schröder, Probability and Mathematical Physics 1 (2020) 101–146. date_created: 2024-03-04T10:27:57Z date_published: 2020-11-16T00:00:00Z date_updated: 2024-03-04T10:33:15Z day: '16' department: - _id: LaEr doi: 10.2140/pmp.2020.1.101 ec_funded: 1 external_id: arxiv: - '1908.01653' intvolume: ' 1' issue: '1' keyword: - General Medicine language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.48550/arXiv.1908.01653 month: '11' oa: 1 oa_version: Preprint page: 101-146 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems - _id: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program publication: Probability and Mathematical Physics publication_identifier: issn: - 2690-1005 - 2690-0998 publication_status: published publisher: Mathematical Sciences Publishers quality_controlled: '1' scopus_import: '1' status: public title: Optimal lower bound on the least singular value of the shifted Ginibre ensemble type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 1 year: '2020' ... --- _id: '15079' abstract: - lang: eng text: "Large complex systems tend to develop universal patterns that often represent their essential characteristics. For example, the cumulative effects of independent or weakly dependent random variables often yield the Gaussian universality class via the central limit theorem. For non-commutative random variables, e.g. matrices, the Gaussian behavior is often replaced by another universality class, commonly called random matrix statistics. Nearby eigenvalues are strongly correlated, and, remarkably, their correlation structure is universal, depending only on the symmetry type of the matrix. Even more surprisingly, this feature is not restricted to matrices; in fact Eugene Wigner, the pioneer of the field, discovered in the 1950s that distributions of the gaps between energy levels of complicated quantum systems universally follow the same random matrix statistics. This claim has never been rigorously proved for any realistic physical system but experimental data and extensive numerics leave no doubt as to its correctness. Since then random matrices have proved to be extremely useful phenomenological models in a wide range of applications beyond quantum physics that include number theory, statistics, neuroscience, population dynamics, wireless communication and mathematical finance. The ubiquity of random matrices in natural sciences is still a mystery, but recent years have witnessed a breakthrough in the mathematical description of the statistical structure of their spectrum. Random matrices and closely related areas such as log-gases have become an extremely active research area in probability theory.\r\nThis workshop brought together outstanding researchers from a variety of mathematical backgrounds whose areas of research are linked to random matrices. While there are strong links between their motivations, the techniques used by these researchers span a large swath of mathematics, ranging from purely algebraic techniques to stochastic analysis, classical probability theory, operator algebra, supersymmetry, orthogonal polynomials, etc." article_processing_charge: No article_type: original author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Friedrich full_name: Götze, Friedrich last_name: Götze - first_name: Alice full_name: Guionnet, Alice last_name: Guionnet citation: ama: Erdös L, Götze F, Guionnet A. Random matrices. Oberwolfach Reports. 2020;16(4):3459-3527. doi:10.4171/owr/2019/56 apa: Erdös, L., Götze, F., & Guionnet, A. (2020). Random matrices. Oberwolfach Reports. European Mathematical Society. https://doi.org/10.4171/owr/2019/56 chicago: Erdös, László, Friedrich Götze, and Alice Guionnet. “Random Matrices.” Oberwolfach Reports. European Mathematical Society, 2020. https://doi.org/10.4171/owr/2019/56. ieee: L. Erdös, F. Götze, and A. Guionnet, “Random matrices,” Oberwolfach Reports, vol. 16, no. 4. European Mathematical Society, pp. 3459–3527, 2020. ista: Erdös L, Götze F, Guionnet A. 2020. Random matrices. Oberwolfach Reports. 16(4), 3459–3527. mla: Erdös, László, et al. “Random Matrices.” Oberwolfach Reports, vol. 16, no. 4, European Mathematical Society, 2020, pp. 3459–527, doi:10.4171/owr/2019/56. short: L. Erdös, F. Götze, A. Guionnet, Oberwolfach Reports 16 (2020) 3459–3527. date_created: 2024-03-05T07:54:44Z date_published: 2020-11-19T00:00:00Z date_updated: 2024-03-12T12:25:18Z day: '19' department: - _id: LaEr doi: 10.4171/owr/2019/56 intvolume: ' 16' issue: '4' language: - iso: eng month: '11' oa_version: None page: 3459-3527 publication: Oberwolfach Reports publication_identifier: issn: - 1660-8933 publication_status: published publisher: European Mathematical Society quality_controlled: '1' status: public title: Random matrices type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 16 year: '2020' ... --- _id: '7035' abstract: - lang: eng text: 'The aim of this short note is to expound one particular issue that was discussed during the talk [10] given at the symposium ”Researches on isometries as preserver problems and related topics” at Kyoto RIMS. That is, the role of Dirac masses by describing the isometry group of various metric spaces of probability measures. This article is of survey character, and it does not contain any essentially new results.From an isometric point of view, in some cases, metric spaces of measures are similar to C(K)-type function spaces. Similarity means here that their isometries are driven by some nice transformations of the underlying space. Of course, it depends on the particular choice of the metric how nice these transformations should be. Sometimes, as we will see, being a homeomorphism is enough to generate an isometry. But sometimes we need more: the transformation must preserve the underlying distance as well. Statements claiming that isometries in questions are necessarily induced by homeomorphisms are called Banach-Stone-type results, while results asserting that the underlying transformation is necessarily an isometry are termed as isometric rigidity results.As Dirac masses can be considered as building bricks of the set of all Borel measures, a natural question arises:Is it enough to understand how an isometry acts on the set of Dirac masses? Does this action extend uniquely to all measures?In what follows, we will thoroughly investigate this question.' article_processing_charge: No author: - first_name: Gyorgy Pal full_name: Geher, Gyorgy Pal last_name: Geher - first_name: Tamas full_name: Titkos, Tamas last_name: Titkos - first_name: Daniel full_name: Virosztek, Daniel id: 48DB45DA-F248-11E8-B48F-1D18A9856A87 last_name: Virosztek orcid: 0000-0003-1109-5511 citation: ama: 'Geher GP, Titkos T, Virosztek D. Dirac masses and isometric rigidity. In: Kyoto RIMS Kôkyûroku. Vol 2125. Research Institute for Mathematical Sciences, Kyoto University; 2019:34-41.' apa: 'Geher, G. P., Titkos, T., & Virosztek, D. (2019). Dirac masses and isometric rigidity. In Kyoto RIMS Kôkyûroku (Vol. 2125, pp. 34–41). Kyoto, Japan: Research Institute for Mathematical Sciences, Kyoto University.' chicago: Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Dirac Masses and Isometric Rigidity.” In Kyoto RIMS Kôkyûroku, 2125:34–41. Research Institute for Mathematical Sciences, Kyoto University, 2019. ieee: G. P. Geher, T. Titkos, and D. Virosztek, “Dirac masses and isometric rigidity,” in Kyoto RIMS Kôkyûroku, Kyoto, Japan, 2019, vol. 2125, pp. 34–41. ista: Geher GP, Titkos T, Virosztek D. 2019. Dirac masses and isometric rigidity. Kyoto RIMS Kôkyûroku. Research on isometries as preserver problems and related topics vol. 2125, 34–41. mla: Geher, Gyorgy Pal, et al. “Dirac Masses and Isometric Rigidity.” Kyoto RIMS Kôkyûroku, vol. 2125, Research Institute for Mathematical Sciences, Kyoto University, 2019, pp. 34–41. short: G.P. Geher, T. Titkos, D. Virosztek, in:, Kyoto RIMS Kôkyûroku, Research Institute for Mathematical Sciences, Kyoto University, 2019, pp. 34–41. conference: end_date: 2019-01-30 location: Kyoto, Japan name: Research on isometries as preserver problems and related topics start_date: 2019-01-28 date_created: 2019-11-18T15:39:53Z date_published: 2019-01-30T00:00:00Z date_updated: 2021-01-12T08:11:33Z day: '30' department: - _id: LaEr intvolume: ' 2125' language: - iso: eng main_file_link: - open_access: '1' url: http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/2125.html month: '01' oa: 1 oa_version: Submitted Version page: 34-41 publication: Kyoto RIMS Kôkyûroku publication_status: published publisher: Research Institute for Mathematical Sciences, Kyoto University quality_controlled: '1' status: public title: Dirac masses and isometric rigidity type: conference user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 2125 year: '2019' ...