[{"issue":"8","abstract":[{"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. ","lang":"eng"}],"type":"journal_article","oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"7618","intvolume":" 110","status":"public","title":"Quantum Hellinger distances revisited","article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2020-08-01T00:00:00Z","citation":{"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.","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.","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","ista":"Pitrik J, Virosztek D. 2020. Quantum Hellinger distances revisited. Letters in Mathematical Physics. 110(8), 2039–2052.","ieee":"J. Pitrik and D. Virosztek, “Quantum Hellinger distances revisited,” Letters in Mathematical Physics, vol. 110, no. 8. Springer Nature, pp. 2039–2052, 2020.","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"},"publication":"Letters in Mathematical Physics","page":"2039-2052","article_type":"original","ec_funded":1,"author":[{"first_name":"Jozsef","last_name":"Pitrik","full_name":"Pitrik, Jozsef"},{"full_name":"Virosztek, Daniel","orcid":"0000-0003-1109-5511","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","last_name":"Virosztek","first_name":"Daniel"}],"volume":110,"date_updated":"2023-08-18T10:17:26Z","date_created":"2020-03-25T15:57:48Z","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.","year":"2020","publisher":"Springer Nature","department":[{"_id":"LaEr"}],"publication_status":"published","publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"month":"08","doi":"10.1007/s11005-020-01282-0","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.10455"}],"external_id":{"isi":["000551556000002"],"arxiv":["1903.10455"]},"oa":1,"project":[{"grant_number":"846294","_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Geometric study of Wasserstein spaces and free probability"},{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","isi":1},{"abstract":[{"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].","lang":"eng"}],"type":"journal_article","oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"9104","intvolume":" 142","title":"On the support of the free additive convolution","status":"public","article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2020-11-01T00:00:00Z","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","ista":"Bao Z, Erdös L, Schnelli K. 2020. On the support of the free additive convolution. Journal d’Analyse Mathematique. 142, 323–348.","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.","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","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.","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."},"publication":"Journal d'Analyse Mathematique","page":"323-348","article_type":"original","ec_funded":1,"author":[{"first_name":"Zhigang","last_name":"Bao","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang"},{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0954-3231","first_name":"Kevin","last_name":"Schnelli","full_name":"Schnelli, Kevin"}],"volume":142,"date_updated":"2023-08-24T11:16:03Z","date_created":"2021-02-07T23:01:15Z","year":"2020","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.","department":[{"_id":"LaEr"}],"publisher":"Springer Nature","publication_status":"published","publication_identifier":{"eissn":["15658538"],"issn":["00217670"]},"month":"11","doi":"10.1007/s11854-020-0135-2","language":[{"iso":"eng"}],"external_id":{"isi":["000611879400008"],"arxiv":["1804.11199"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1804.11199","open_access":"1"}],"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"}],"isi":1,"quality_controlled":"1"},{"oa_version":"Preprint","intvolume":" 279","status":"public","title":"Spectral rigidity for addition of random matrices at the regular edge","_id":"10862","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","issue":"7","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."}],"type":"journal_article","date_published":"2020-10-15T00:00:00Z","article_type":"original","citation":{"short":"Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 279 (2020).","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.","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.","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","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.","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","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."},"publication":"Journal of Functional Analysis","article_processing_charge":"No","day":"15","keyword":["Analysis"],"scopus_import":"1","volume":279,"date_created":"2022-03-18T10:18:59Z","date_updated":"2023-08-24T14:08:42Z","author":[{"full_name":"Bao, Zhigang","last_name":"Bao","first_name":"Zhigang","orcid":"0000-0003-3036-1475","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"first_name":"Kevin","last_name":"Schnelli","full_name":"Schnelli, Kevin"}],"department":[{"_id":"LaEr"}],"publisher":"Elsevier","publication_status":"published","year":"2020","acknowledgement":"Partially supported by ERC Advanced Grant RANMAT No. 338804.","ec_funded":1,"article_number":"108639","language":[{"iso":"eng"}],"doi":"10.1016/j.jfa.2020.108639","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","isi":1,"external_id":{"arxiv":["1708.01597"],"isi":["000559623200009"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1708.01597","open_access":"1"}],"publication_identifier":{"issn":["0022-1236"]},"month":"10"},{"language":[{"iso":"eng"}],"doi":"10.1142/S2010326320500069","isi":1,"quality_controlled":"1","project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"name":"International IST Doctoral Program","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385"}],"external_id":{"arxiv":["1806.08751"],"isi":["000547464400001"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1806.08751"}],"month":"07","publication_identifier":{"issn":["20103263"],"eissn":["20103271"]},"date_created":"2019-05-26T21:59:14Z","date_updated":"2023-08-28T08:38:48Z","volume":9,"author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","first_name":"Giorgio"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"}],"publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"World Scientific Publishing","year":"2020","ec_funded":1,"article_number":"2050006","date_published":"2020-07-01T00:00:00Z","article_type":"original","publication":"Random Matrices: Theory and Application","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","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.","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.","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","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).","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."},"day":"01","article_processing_charge":"No","scopus_import":"1","oa_version":"Preprint","status":"public","title":"Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices","intvolume":" 9","_id":"6488","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","abstract":[{"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.","lang":"eng"}],"issue":"3","type":"journal_article"},{"file_date_updated":"2020-11-18T11:14:37Z","ec_funded":1,"year":"2020","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.","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"LaEr"}],"author":[{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"Krüger, Torben H","first_name":"Torben H","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","first_name":"Dominik J"}],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"6179"}]},"date_updated":"2023-09-07T12:54:12Z","date_created":"2019-03-28T10:21:15Z","volume":378,"month":"09","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["1809.03971"],"isi":["000529483000001"]},"quality_controlled":"1","isi":1,"project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"doi":"10.1007/s00220-019-03657-4","language":[{"iso":"eng"}],"type":"journal_article","abstract":[{"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).","lang":"eng"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6185","ddc":["530","510"],"status":"public","title":"Cusp universality for random matrices I: Local law and the complex Hermitian case","intvolume":" 378","file":[{"access_level":"open_access","file_name":"2020_CommMathPhysics_Erdoes.pdf","file_size":2904574,"content_type":"application/pdf","creator":"dernst","relation":"main_file","file_id":"8771","checksum":"c3a683e2afdcea27afa6880b01e53dc2","success":1,"date_updated":"2020-11-18T11:14:37Z","date_created":"2020-11-18T11:14:37Z"}],"oa_version":"Published Version","scopus_import":"1","day":"01","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","publication":"Communications in Mathematical Physics","citation":{"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.","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","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.","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","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.","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."},"article_type":"original","page":"1203-1278","date_published":"2020-09-01T00:00:00Z"},{"type":"journal_article","abstract":[{"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.","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"14694","intvolume":" 25","title":"The Dyson equation with linear self-energy: Spectral bands, edges and cusps","status":"public","ddc":["510"],"oa_version":"Published Version","file":[{"relation":"main_file","file_id":"14695","date_updated":"2023-12-18T10:42:32Z","date_created":"2023-12-18T10:42:32Z","checksum":"12aacc1d63b852ff9a51c1f6b218d4a6","success":1,"file_name":"2020_DocumentaMathematica_Alt.pdf","access_level":"open_access","content_type":"application/pdf","file_size":1374708,"creator":"dernst"}],"keyword":["General Mathematics"],"has_accepted_license":"1","article_processing_charge":"Yes","day":"01","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","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.","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.","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","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.","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."},"publication":"Documenta Mathematica","page":"1421-1539","article_type":"original","date_published":"2020-09-01T00:00:00Z","file_date_updated":"2023-12-18T10:42:32Z","year":"2020","department":[{"_id":"LaEr"}],"publisher":"EMS Press","publication_status":"published","related_material":{"record":[{"id":"6183","status":"public","relation":"earlier_version"}]},"author":[{"id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","first_name":"Johannes","last_name":"Alt","full_name":"Alt, Johannes"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"full_name":"Krüger, Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","first_name":"Torben H","last_name":"Krüger"}],"volume":25,"date_created":"2023-12-18T10:37:43Z","date_updated":"2023-12-18T10:46:09Z","publication_identifier":{"eissn":["1431-0643"],"issn":["1431-0635"]},"month":"09","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["1804.07752"]},"quality_controlled":"1","doi":"10.4171/dm/780","language":[{"iso":"eng"}]},{"publication_identifier":{"issn":["0091-1798"]},"month":"03","language":[{"iso":"eng"}],"doi":"10.1214/19-AOP1379","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"quality_controlled":"1","isi":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.07744"}],"oa":1,"external_id":{"arxiv":["1804.07744"],"isi":["000528269100013"]},"ec_funded":1,"volume":48,"date_created":"2019-03-28T09:20:08Z","date_updated":"2024-02-22T14:34:33Z","related_material":{"record":[{"id":"149","relation":"dissertation_contains","status":"public"},{"id":"6179","status":"public","relation":"dissertation_contains"}]},"author":[{"id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","last_name":"Alt","first_name":"Johannes","full_name":"Alt, Johannes"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"},{"last_name":"Krüger","first_name":"Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H"},{"first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"publication_status":"published","year":"2020","article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2020-03-01T00:00:00Z","page":"963-1001","article_type":"original","citation":{"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.","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.","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","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","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.","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."},"publication":"Annals of Probability","issue":"2","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."}],"type":"journal_article","oa_version":"Preprint","intvolume":" 48","title":"Correlated random matrices: Band rigidity and edge universality","status":"public","_id":"6184","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87"},{"external_id":{"arxiv":["1908.01653"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1908.01653","open_access":"1"}],"oa":1,"project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"},{"grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"International IST Doctoral Program"}],"quality_controlled":"1","doi":"10.2140/pmp.2020.1.101","language":[{"iso":"eng"}],"publication_identifier":{"issn":["2690-1005","2690-0998"]},"month":"11","year":"2020","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","department":[{"_id":"LaEr"}],"publisher":"Mathematical Sciences Publishers","publication_status":"published","author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","first_name":"Giorgio","last_name":"Cipolloni"},{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","first_name":"Dominik J","last_name":"Schröder","full_name":"Schröder, Dominik J"}],"volume":1,"date_created":"2024-03-04T10:27:57Z","date_updated":"2024-03-04T10:33:15Z","ec_funded":1,"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","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.","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","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.","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.","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."},"publication":"Probability and Mathematical Physics","page":"101-146","article_type":"original","date_published":"2020-11-16T00:00:00Z","scopus_import":"1","keyword":["General Medicine"],"article_processing_charge":"No","day":"16","_id":"15063","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 1","status":"public","title":"Optimal lower bound on the least singular value of the shifted Ginibre ensemble","oa_version":"Preprint","type":"journal_article","issue":"1","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)."}]},{"author":[{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"last_name":"Götze","first_name":"Friedrich","full_name":"Götze, Friedrich"},{"last_name":"Guionnet","first_name":"Alice","full_name":"Guionnet, Alice"}],"oa_version":"None","volume":16,"date_updated":"2024-03-12T12:25:18Z","date_created":"2024-03-05T07:54:44Z","year":"2020","_id":"15079","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"European Mathematical Society","department":[{"_id":"LaEr"}],"intvolume":" 16","title":"Random matrices","status":"public","publication_status":"published","issue":"4","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."}],"type":"journal_article","doi":"10.4171/owr/2019/56","date_published":"2020-11-19T00:00:00Z","language":[{"iso":"eng"}],"citation":{"ista":"Erdös L, Götze F, Guionnet A. 2020. Random matrices. Oberwolfach Reports. 16(4), 3459–3527.","ieee":"L. Erdös, F. Götze, and A. Guionnet, “Random matrices,” Oberwolfach Reports, vol. 16, no. 4. European Mathematical Society, pp. 3459–3527, 2020.","apa":"Erdös, L., Götze, F., & Guionnet, A. (2020). Random matrices. Oberwolfach Reports. European Mathematical Society. https://doi.org/10.4171/owr/2019/56","ama":"Erdös L, Götze F, Guionnet A. Random matrices. Oberwolfach Reports. 2020;16(4):3459-3527. doi: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.","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."},"publication":"Oberwolfach Reports","page":"3459-3527","article_type":"original","quality_controlled":"1","article_processing_charge":"No","publication_identifier":{"issn":["1660-8933"]},"month":"11","day":"19"},{"type":"conference","abstract":[{"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.","lang":"eng"}],"publication_status":"published","title":"Dirac masses and isometric rigidity","status":"public","publisher":"Research Institute for Mathematical Sciences, Kyoto University","intvolume":" 2125","department":[{"_id":"LaEr"}],"_id":"7035","year":"2019","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2019-11-18T15:39:53Z","date_updated":"2021-01-12T08:11:33Z","oa_version":"Submitted Version","volume":2125,"author":[{"last_name":"Geher","first_name":"Gyorgy Pal","full_name":"Geher, Gyorgy Pal"},{"full_name":"Titkos, Tamas","first_name":"Tamas","last_name":"Titkos"},{"full_name":"Virosztek, Daniel","last_name":"Virosztek","first_name":"Daniel","orcid":"0000-0003-1109-5511","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"month":"01","day":"30","article_processing_charge":"No","quality_controlled":"1","page":"34-41","publication":"Kyoto RIMS Kôkyûroku","oa":1,"main_file_link":[{"url":"http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/2125.html","open_access":"1"}],"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.","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.","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.","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.","short":"G.P. Geher, T. Titkos, D. Virosztek, in:, Kyoto RIMS Kôkyûroku, Research Institute for Mathematical Sciences, Kyoto University, 2019, pp. 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.","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."},"language":[{"iso":"eng"}],"conference":{"name":"Research on isometries as preserver problems and related topics","end_date":"2019-01-30","start_date":"2019-01-28","location":"Kyoto, Japan"},"date_published":"2019-01-30T00:00:00Z"},{"publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Formal Power Series and Algebraic Combinatorics","year":"2019","acknowledgement":"D.B. is especially grateful to Patrik Ferrari for suggesting simplifications in Section 3 and\r\nto Alessandra Occelli for suggesting the name for the models of Section 2.\r\n","date_updated":"2021-01-12T08:17:18Z","date_created":"2020-07-26T22:01:04Z","author":[{"last_name":"Betea","first_name":"Dan","full_name":"Betea, Dan"},{"full_name":"Bouttier, Jérémie","first_name":"Jérémie","last_name":"Bouttier"},{"id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","first_name":"Peter","last_name":"Nejjar","full_name":"Nejjar, Peter"},{"first_name":"Mirjana","last_name":"Vuletíc","full_name":"Vuletíc, Mirjana"}],"article_number":"34","ec_funded":1,"quality_controlled":"1","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"},{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117"}],"main_file_link":[{"url":"https://arxiv.org/abs/1902.08750","open_access":"1"}],"external_id":{"arxiv":["1902.08750"]},"oa":1,"language":[{"iso":"eng"}],"conference":{"name":"FPSAC: International Conference on Formal Power Series and Algebraic Combinatorics","start_date":"2019-07-01","location":"Ljubljana, Slovenia","end_date":"2019-07-05"},"month":"07","title":"New edge asymptotics of skew Young diagrams via free boundaries","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"8175","oa_version":"Preprint","type":"conference","abstract":[{"lang":"eng","text":"We study edge asymptotics of poissonized Plancherel-type measures on skew Young diagrams (integer partitions). These measures can be seen as generalizations of those studied by Baik--Deift--Johansson and Baik--Rains in resolving Ulam's problem on longest increasing subsequences of random permutations and the last passage percolation (corner growth) discrete versions thereof. Moreover they interpolate between said measures and the uniform measure on partitions. In the new KPZ-like 1/3 exponent edge scaling limit with logarithmic corrections, we find new probability distributions generalizing the classical Tracy--Widom GUE, GOE and GSE distributions from the theory of random matrices."}],"publication":"Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics","citation":{"ama":"Betea D, Bouttier J, Nejjar P, Vuletíc M. New edge asymptotics of skew Young diagrams via free boundaries. In: Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. Formal Power Series and Algebraic Combinatorics; 2019.","ista":"Betea D, Bouttier J, Nejjar P, Vuletíc M. 2019. New edge asymptotics of skew Young diagrams via free boundaries. Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. FPSAC: International Conference on Formal Power Series and Algebraic Combinatorics, 34.","apa":"Betea, D., Bouttier, J., Nejjar, P., & Vuletíc, M. (2019). New edge asymptotics of skew Young diagrams via free boundaries. In Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. Ljubljana, Slovenia: Formal Power Series and Algebraic Combinatorics.","ieee":"D. Betea, J. Bouttier, P. Nejjar, and M. Vuletíc, “New edge asymptotics of skew Young diagrams via free boundaries,” in Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics, Ljubljana, Slovenia, 2019.","mla":"Betea, Dan, et al. “New Edge Asymptotics of Skew Young Diagrams via Free Boundaries.” Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics, 34, Formal Power Series and Algebraic Combinatorics, 2019.","short":"D. Betea, J. Bouttier, P. Nejjar, M. Vuletíc, in:, Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics, Formal Power Series and Algebraic Combinatorics, 2019.","chicago":"Betea, Dan, Jérémie Bouttier, Peter Nejjar, and Mirjana Vuletíc. “New Edge Asymptotics of Skew Young Diagrams via Free Boundaries.” In Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. Formal Power Series and Algebraic Combinatorics, 2019."},"date_published":"2019-07-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No"},{"month":"09","language":[{"iso":"eng"}],"doi":"10.1016/j.laa.2018.03.002","isi":1,"quality_controlled":"1","project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1712.05324"}],"external_id":{"isi":["000470955300005"],"arxiv":["1712.05324"]},"publist_id":"7424","ec_funded":1,"date_created":"2018-12-11T11:46:17Z","date_updated":"2023-08-24T14:31:47Z","volume":576,"author":[{"first_name":"Daniel","last_name":"Virosztek","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel"}],"publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Elsevier","year":"2019","acknowledgement":"The author was supported by the ISTFELLOW program of the Institute of Science and Technology Austria (project code IC1027FELL01) and partially supported by the Hungarian National Research, Development and Innovation Office – NKFIH (grant no. K124152)","day":"01","article_processing_charge":"No","scopus_import":"1","date_published":"2019-09-01T00:00:00Z","article_type":"original","page":"67-78","publication":"Linear Algebra and Its Applications","citation":{"apa":"Virosztek, D. (2019). Jointly convex quantum Jensen divergences. Linear Algebra and Its Applications. Elsevier. https://doi.org/10.1016/j.laa.2018.03.002","ieee":"D. Virosztek, “Jointly convex quantum Jensen divergences,” Linear Algebra and Its Applications, vol. 576. Elsevier, pp. 67–78, 2019.","ista":"Virosztek D. 2019. Jointly convex quantum Jensen divergences. Linear Algebra and Its Applications. 576, 67–78.","ama":"Virosztek D. Jointly convex quantum Jensen divergences. Linear Algebra and Its Applications. 2019;576:67-78. doi:10.1016/j.laa.2018.03.002","chicago":"Virosztek, Daniel. “Jointly Convex Quantum Jensen Divergences.” Linear Algebra and Its Applications. Elsevier, 2019. https://doi.org/10.1016/j.laa.2018.03.002.","short":"D. Virosztek, Linear Algebra and Its Applications 576 (2019) 67–78.","mla":"Virosztek, Daniel. “Jointly Convex Quantum Jensen Divergences.” Linear Algebra and Its Applications, vol. 576, Elsevier, 2019, pp. 67–78, doi:10.1016/j.laa.2018.03.002."},"abstract":[{"text":"We investigate the quantum Jensen divergences from the viewpoint of joint convexity. It turns out that the set of the functions which generate jointly convex quantum Jensen divergences on positive matrices coincides with the Matrix Entropy Class which has been introduced by Chen and Tropp quite recently.","lang":"eng"}],"type":"journal_article","oa_version":"Preprint","title":"Jointly convex quantum Jensen divergences","status":"public","intvolume":" 576","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"405"},{"month":"02","publication_identifier":{"issn":["01788051"],"eissn":["14322064"]},"external_id":{"isi":["000459396500007"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"isi":1,"quality_controlled":"1","project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"doi":"10.1007/s00440-018-0835-z","language":[{"iso":"eng"}],"file_date_updated":"2020-07-14T12:46:26Z","publist_id":"7394","ec_funded":1,"year":"2019","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).\r\n","publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Springer","author":[{"id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87","last_name":"Ajanki","first_name":"Oskari H","full_name":"Ajanki, Oskari H"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"Erdös, László"},{"full_name":"Krüger, Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","first_name":"Torben H","last_name":"Krüger"}],"date_created":"2018-12-11T11:46:25Z","date_updated":"2023-08-24T14:39:00Z","volume":173,"scopus_import":"1","day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","publication":"Probability Theory and Related Fields","citation":{"short":"O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields 173 (2019) 293–373.","mla":"Ajanki, Oskari H., et al. “Stability of the Matrix Dyson Equation and Random Matrices with Correlations.” Probability Theory and Related Fields, vol. 173, no. 1–2, Springer, 2019, pp. 293–373, doi:10.1007/s00440-018-0835-z.","chicago":"Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Stability of the Matrix Dyson Equation and Random Matrices with Correlations.” Probability Theory and Related Fields. Springer, 2019. https://doi.org/10.1007/s00440-018-0835-z.","ama":"Ajanki OH, Erdös L, Krüger TH. Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. 2019;173(1-2):293–373. doi:10.1007/s00440-018-0835-z","apa":"Ajanki, O. H., Erdös, L., & Krüger, T. H. (2019). Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-018-0835-z","ieee":"O. H. Ajanki, L. Erdös, and T. H. Krüger, “Stability of the matrix Dyson equation and random matrices with correlations,” Probability Theory and Related Fields, vol. 173, no. 1–2. Springer, pp. 293–373, 2019.","ista":"Ajanki OH, Erdös L, Krüger TH. 2019. Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. 173(1–2), 293–373."},"article_type":"original","page":"293–373","date_published":"2019-02-01T00:00:00Z","type":"journal_article","abstract":[{"text":"We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay but are otherwise of general form. The key novelty is the detailed stability analysis of the corresponding matrix valued Dyson equation whose solution is the deterministic limit of the resolvent.","lang":"eng"}],"issue":"1-2","_id":"429","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","ddc":["510"],"title":"Stability of the matrix Dyson equation and random matrices with correlations","status":"public","intvolume":" 173","oa_version":"Published Version","file":[{"checksum":"f9354fa5c71f9edd17132588f0dc7d01","date_created":"2018-12-17T16:12:08Z","date_updated":"2020-07-14T12:46:26Z","relation":"main_file","file_id":"5720","file_size":1201840,"content_type":"application/pdf","creator":"dernst","access_level":"open_access","file_name":"2018_ProbTheory_Ajanki.pdf"}]},{"ec_funded":1,"year":"2019","publisher":"Cambridge University Press","department":[{"_id":"LaEr"}],"publication_status":"published","author":[{"first_name":"Christian","last_name":"Sadel","id":"4760E9F8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8255-3968","full_name":"Sadel, Christian"},{"first_name":"Disheng","last_name":"Xu","full_name":"Xu, Disheng"}],"volume":39,"date_created":"2019-03-10T22:59:18Z","date_updated":"2023-08-25T08:03:30Z","month":"04","external_id":{"arxiv":["1601.06118"],"isi":["000459725600012"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1601.06118","open_access":"1"}],"project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"isi":1,"quality_controlled":"1","doi":"10.1017/etds.2017.52","language":[{"iso":"eng"}],"type":"journal_article","issue":"4","abstract":[{"lang":"eng","text":"We show that linear analytic cocycles where all Lyapunov exponents are negative infinite are nilpotent. For such one-frequency cocycles we show that they can be analytically conjugated to an upper triangular cocycle or a Jordan normal form. As a consequence, an arbitrarily small analytic perturbation leads to distinct Lyapunov exponents. Moreover, in the one-frequency case where the th Lyapunov exponent is finite and the st negative infinite, we obtain a simple criterion for domination in which case there is a splitting into a nilpotent part and an invertible part."}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6086","intvolume":" 39","title":"Singular analytic linear cocycles with negative infinite Lyapunov exponents","status":"public","oa_version":"Preprint","scopus_import":"1","article_processing_charge":"No","day":"01","citation":{"chicago":"Sadel, Christian, and Disheng Xu. “Singular Analytic Linear Cocycles with Negative Infinite Lyapunov Exponents.” Ergodic Theory and Dynamical Systems. Cambridge University Press, 2019. https://doi.org/10.1017/etds.2017.52.","short":"C. Sadel, D. Xu, Ergodic Theory and Dynamical Systems 39 (2019) 1082–1098.","mla":"Sadel, Christian, and Disheng Xu. “Singular Analytic Linear Cocycles with Negative Infinite Lyapunov Exponents.” Ergodic Theory and Dynamical Systems, vol. 39, no. 4, Cambridge University Press, 2019, pp. 1082–98, doi:10.1017/etds.2017.52.","apa":"Sadel, C., & Xu, D. (2019). Singular analytic linear cocycles with negative infinite Lyapunov exponents. Ergodic Theory and Dynamical Systems. Cambridge University Press. https://doi.org/10.1017/etds.2017.52","ieee":"C. Sadel and D. Xu, “Singular analytic linear cocycles with negative infinite Lyapunov exponents,” Ergodic Theory and Dynamical Systems, vol. 39, no. 4. Cambridge University Press, pp. 1082–1098, 2019.","ista":"Sadel C, Xu D. 2019. Singular analytic linear cocycles with negative infinite Lyapunov exponents. Ergodic Theory and Dynamical Systems. 39(4), 1082–1098.","ama":"Sadel C, Xu D. Singular analytic linear cocycles with negative infinite Lyapunov exponents. Ergodic Theory and Dynamical Systems. 2019;39(4):1082-1098. doi:10.1017/etds.2017.52"},"publication":"Ergodic Theory and Dynamical Systems","page":"1082-1098","date_published":"2019-04-01T00:00:00Z"},{"scopus_import":"1","article_processing_charge":"No","day":"01","page":"1270-1334","citation":{"ista":"Bao Z, Erdös L, Schnelli K. 2019. Local single ring theorem on optimal scale. Annals of Probability. 47(3), 1270–1334.","apa":"Bao, Z., Erdös, L., & Schnelli, K. (2019). Local single ring theorem on optimal scale. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/18-AOP1284","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Local single ring theorem on optimal scale,” Annals of Probability, vol. 47, no. 3. Institute of Mathematical Statistics, pp. 1270–1334, 2019.","ama":"Bao Z, Erdös L, Schnelli K. Local single ring theorem on optimal scale. Annals of Probability. 2019;47(3):1270-1334. doi:10.1214/18-AOP1284","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Single Ring Theorem on Optimal Scale.” Annals of Probability. Institute of Mathematical Statistics, 2019. https://doi.org/10.1214/18-AOP1284.","mla":"Bao, Zhigang, et al. “Local Single Ring Theorem on Optimal Scale.” Annals of Probability, vol. 47, no. 3, Institute of Mathematical Statistics, 2019, pp. 1270–334, doi:10.1214/18-AOP1284.","short":"Z. Bao, L. Erdös, K. Schnelli, Annals of Probability 47 (2019) 1270–1334."},"publication":"Annals of Probability","date_published":"2019-05-01T00:00:00Z","type":"journal_article","issue":"3","abstract":[{"text":"Let U and V be two independent N by N random matrices that are distributed according to Haar measure on U(N). Let Σ be a nonnegative deterministic N by N matrix. The single ring theorem [Ann. of Math. (2) 174 (2011) 1189–1217] asserts that the empirical eigenvalue distribution of the matrix X:=UΣV∗ converges weakly, in the limit of large N, to a deterministic measure which is supported on a single ring centered at the origin in ℂ. Within the bulk regime, that is, in the interior of the single ring, we establish the convergence of the empirical eigenvalue distribution on the optimal local scale of order N−1/2+ε and establish the optimal convergence rate. The same results hold true when U and V are Haar distributed on O(N).","lang":"eng"}],"intvolume":" 47","status":"public","title":"Local single ring theorem on optimal scale","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6511","oa_version":"Preprint","publication_identifier":{"issn":["00911798"]},"month":"05","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"}],"quality_controlled":"1","isi":1,"external_id":{"isi":["000466616100003"],"arxiv":["1612.05920"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1612.05920","open_access":"1"}],"language":[{"iso":"eng"}],"doi":"10.1214/18-AOP1284","ec_funded":1,"publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"publication_status":"published","year":"2019","volume":47,"date_updated":"2023-08-28T09:32:29Z","date_created":"2019-06-02T21:59:13Z","author":[{"last_name":"Bao","first_name":"Zhigang","orcid":"0000-0003-3036-1475","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","full_name":"Bao, Zhigang"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","full_name":"Erdös, László"},{"first_name":"Kevin","last_name":"Schnelli","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin"}]},{"oa_version":"Preprint","_id":"6843","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 480","status":"public","title":"On isometric embeddings of Wasserstein spaces – the discrete case","issue":"2","abstract":[{"text":"The aim of this short paper is to offer a complete characterization of all (not necessarily surjective) isometric embeddings of the Wasserstein space Wp(X), where S is a countable discrete metric space and 0
Journal of Mathematical Analysis and Applications. Elsevier, 2019. https://doi.org/10.1016/j.jmaa.2019.123435.","short":"G.P. Gehér, T. Titkos, D. Virosztek, Journal of Mathematical Analysis and Applications 480 (2019).","mla":"Gehér, György Pál, et al. “On Isometric Embeddings of Wasserstein Spaces – the Discrete Case.” Journal of Mathematical Analysis and Applications, vol. 480, no. 2, 123435, Elsevier, 2019, doi:10.1016/j.jmaa.2019.123435.","ieee":"G. P. Gehér, T. Titkos, and D. Virosztek, “On isometric embeddings of Wasserstein spaces – the discrete case,” Journal of Mathematical Analysis and Applications, vol. 480, no. 2. Elsevier, 2019.","apa":"Gehér, G. P., Titkos, T., & Virosztek, D. (2019). On isometric embeddings of Wasserstein spaces – the discrete case. Journal of Mathematical Analysis and Applications. Elsevier. https://doi.org/10.1016/j.jmaa.2019.123435","ista":"Gehér GP, Titkos T, Virosztek D. 2019. On isometric embeddings of Wasserstein spaces – the discrete case. Journal of Mathematical Analysis and Applications. 480(2), 123435.","ama":"Gehér GP, Titkos T, Virosztek D. On isometric embeddings of Wasserstein spaces – the discrete case. Journal of Mathematical Analysis and Applications. 2019;480(2). doi:10.1016/j.jmaa.2019.123435"},"publication":"Journal of Mathematical Analysis and Applications","article_type":"original","article_processing_charge":"No","day":"15","scopus_import":"1","author":[{"full_name":"Gehér, György Pál","first_name":"György Pál","last_name":"Gehér"},{"full_name":"Titkos, Tamás","last_name":"Titkos","first_name":"Tamás"},{"full_name":"Virosztek, Daniel","first_name":"Daniel","last_name":"Virosztek","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-1109-5511"}],"volume":480,"date_created":"2019-09-01T22:01:01Z","date_updated":"2023-08-29T07:18:50Z","year":"2019","publisher":"Elsevier","department":[{"_id":"LaEr"}],"publication_status":"published","ec_funded":1,"article_number":"123435","doi":"10.1016/j.jmaa.2019.123435","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1809.01101","open_access":"1"}],"oa":1,"external_id":{"isi":["000486563900031"],"arxiv":["1809.01101"]},"project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"quality_controlled":"1","isi":1,"publication_identifier":{"eissn":["10960813"],"issn":["0022247X"]},"month":"12"},{"isi":1,"quality_controlled":"1","external_id":{"arxiv":["1704.05224"],"isi":["000456070200013"]},"main_file_link":[{"url":"https://arxiv.org/abs/1704.05224","open_access":"1"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1214/18-aihp888","month":"02","publication_identifier":{"issn":["0246-0203"]},"publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","year":"2019","date_created":"2020-01-30T10:36:50Z","date_updated":"2023-09-06T14:58:39Z","volume":55,"author":[{"first_name":"Gernot","last_name":"Akemann","full_name":"Akemann, Gernot"},{"full_name":"Checinski, Tomasz","first_name":"Tomasz","last_name":"Checinski"},{"full_name":"Liu, Dangzheng","id":"2F947E34-F248-11E8-B48F-1D18A9856A87","first_name":"Dangzheng","last_name":"Liu"},{"last_name":"Strahov","first_name":"Eugene","full_name":"Strahov, Eugene"}],"article_type":"original","page":"441-479","publication":"Annales de l'Institut Henri Poincaré, Probabilités et Statistiques","citation":{"chicago":"Akemann, Gernot, Tomasz Checinski, Dangzheng Liu, and Eugene Strahov. “Finite Rank Perturbations in Products of Coupled Random Matrices: From One Correlated to Two Wishart Ensembles.” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. Institute of Mathematical Statistics, 2019. https://doi.org/10.1214/18-aihp888.","short":"G. Akemann, T. Checinski, D. Liu, E. Strahov, Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55 (2019) 441–479.","mla":"Akemann, Gernot, et al. “Finite Rank Perturbations in Products of Coupled Random Matrices: From One Correlated to Two Wishart Ensembles.” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, vol. 55, no. 1, Institute of Mathematical Statistics, 2019, pp. 441–79, doi:10.1214/18-aihp888.","ieee":"G. Akemann, T. Checinski, D. Liu, and E. Strahov, “Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles,” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, vol. 55, no. 1. Institute of Mathematical Statistics, pp. 441–479, 2019.","apa":"Akemann, G., Checinski, T., Liu, D., & Strahov, E. (2019). Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. Institute of Mathematical Statistics. https://doi.org/10.1214/18-aihp888","ista":"Akemann G, Checinski T, Liu D, Strahov E. 2019. Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. 55(1), 441–479.","ama":"Akemann G, Checinski T, Liu D, Strahov E. Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. 2019;55(1):441-479. doi:10.1214/18-aihp888"},"date_published":"2019-02-01T00:00:00Z","day":"01","article_processing_charge":"No","status":"public","title":"Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles","intvolume":" 55","_id":"7423","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Preprint","type":"journal_article","abstract":[{"text":"We compare finite rank perturbations of the following three ensembles of complex rectangular random matrices: First, a generalised Wishart ensemble with one random and two fixed correlation matrices introduced by Borodin and Péché, second, the product of two independent random matrices where one has correlated entries, and third, the case when the two random matrices become also coupled through a fixed matrix. The singular value statistics of all three ensembles is shown to be determinantal and we derive double contour integral representations for their respective kernels. Three different kernels are found in the limit of infinite matrix dimension at the origin of the spectrum. They depend on finite rank perturbations of the correlation and coupling matrices and are shown to be integrable. The first kernel (I) is found for two independent matrices from the second, and two weakly coupled matrices from the third ensemble. It generalises the Meijer G-kernel for two independent and uncorrelated matrices. The third kernel (III) is obtained for the generalised Wishart ensemble and for two strongly coupled matrices. It further generalises the perturbed Bessel kernel of Desrosiers and Forrester. Finally, kernel (II), found for the ensemble of two coupled matrices, provides an interpolation between the kernels (I) and (III), generalising previous findings of part of the authors.","lang":"eng"}],"issue":"1"},{"volume":7,"date_updated":"2023-09-07T12:54:12Z","date_created":"2019-03-28T09:05:23Z","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"6179"}]},"author":[{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","last_name":"Krüger","first_name":"Torben H"},{"orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","first_name":"Dominik J","full_name":"Schröder, Dominik J"}],"department":[{"_id":"LaEr"}],"publisher":"Cambridge University Press","publication_status":"published","year":"2019","ec_funded":1,"file_date_updated":"2020-07-14T12:47:22Z","article_number":"e8","language":[{"iso":"eng"}],"doi":"10.1017/fms.2019.2","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"isi":1,"quality_controlled":"1","external_id":{"isi":["000488847100001"],"arxiv":["1705.10661"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"publication_identifier":{"eissn":["20505094"]},"month":"03","oa_version":"Published Version","file":[{"file_name":"2019_Forum_Erdoes.pdf","access_level":"open_access","creator":"dernst","content_type":"application/pdf","file_size":1520344,"file_id":"6883","relation":"main_file","date_updated":"2020-07-14T12:47:22Z","date_created":"2019-09-17T14:24:13Z","checksum":"933a472568221c73b2c3ce8c87bf6d15"}],"intvolume":" 7","ddc":["510"],"status":"public","title":"Random matrices with slow correlation decay","_id":"6182","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","abstract":[{"text":"We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the recent result of Ajanki et al. [‘Stability of the matrix Dyson equation and random matrices with correlations’, Probab. Theory Related Fields 173(1–2) (2019), 293–373] to allow slow correlation decay and arbitrary expectation. The main novel tool is\r\na systematic diagrammatic control of a multivariate cumulant expansion.","lang":"eng"}],"type":"journal_article","date_published":"2019-03-26T00:00:00Z","article_type":"original","citation":{"ista":"Erdös L, Krüger TH, Schröder DJ. 2019. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 7, e8.","apa":"Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Random matrices with slow correlation decay. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2019.2","ieee":"L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation decay,” Forum of Mathematics, Sigma, vol. 7. Cambridge University Press, 2019.","ama":"Erdös L, Krüger TH, Schröder DJ. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 2019;7. doi:10.1017/fms.2019.2","chicago":"Erdös, László, Torben H Krüger, and Dominik J Schröder. “Random Matrices with Slow Correlation Decay.” Forum of Mathematics, Sigma. Cambridge University Press, 2019. https://doi.org/10.1017/fms.2019.2.","mla":"Erdös, László, et al. “Random Matrices with Slow Correlation Decay.” Forum of Mathematics, Sigma, vol. 7, e8, Cambridge University Press, 2019, doi:10.1017/fms.2019.2.","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Forum of Mathematics, Sigma 7 (2019)."},"publication":"Forum of Mathematics, Sigma","article_processing_charge":"No","has_accepted_license":"1","day":"26","scopus_import":"1"},{"citation":{"chicago":"Cipolloni, Giorgio, László Erdös, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” Pure and Applied Analysis . MSP, 2019. https://doi.org/10.2140/paa.2019.1.615.","mla":"Cipolloni, Giorgio, et al. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” Pure and Applied Analysis , vol. 1, no. 4, MSP, 2019, pp. 615–707, doi:10.2140/paa.2019.1.615.","short":"G. Cipolloni, L. Erdös, T.H. Krüger, D.J. Schröder, Pure and Applied Analysis 1 (2019) 615–707.","ista":"Cipolloni G, Erdös L, Krüger TH, Schröder DJ. 2019. Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . 1(4), 615–707.","apa":"Cipolloni, G., Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . MSP. https://doi.org/10.2140/paa.2019.1.615","ieee":"G. Cipolloni, L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices, II: The real symmetric case,” Pure and Applied Analysis , vol. 1, no. 4. MSP, pp. 615–707, 2019.","ama":"Cipolloni G, Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . 2019;1(4):615–707. doi:10.2140/paa.2019.1.615"},"publication":"Pure and Applied Analysis ","page":"615–707","article_type":"original","date_published":"2019-10-12T00:00:00Z","article_processing_charge":"No","day":"12","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"6186","intvolume":" 1","title":"Cusp universality for random matrices, II: The real symmetric case","status":"public","oa_version":"Preprint","type":"journal_article","issue":"4","abstract":[{"lang":"eng","text":"We prove that the local eigenvalue statistics of real symmetric Wigner-type\r\nmatrices near the cusp points of the eigenvalue density are universal. Together\r\nwith the companion paper [arXiv:1809.03971], which proves the same result for\r\nthe complex Hermitian symmetry class, this completes the last remaining case of\r\nthe Wigner-Dyson-Mehta universality conjecture after bulk and edge\r\nuniversalities have been established in the last years. We extend the recent\r\nDyson Brownian motion analysis at the edge [arXiv:1712.03881] to the cusp\r\nregime using the optimal local law from [arXiv:1809.03971] and the accurate\r\nlocal shape analysis of the density from [arXiv:1506.05095, arXiv:1804.07752].\r\nWe also present a PDE-based method to improve the estimate on eigenvalue\r\nrigidity via the maximum principle of the heat flow related to the Dyson\r\nBrownian motion."}],"oa":1,"external_id":{"arxiv":["1811.04055"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1811.04055"}],"project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"},{"grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","name":"International IST Doctoral Program","call_identifier":"H2020"}],"quality_controlled":"1","doi":"10.2140/paa.2019.1.615","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["2578-5885"],"issn":["2578-5893"]},"month":"10","year":"2019","publisher":"MSP","department":[{"_id":"LaEr"}],"publication_status":"published","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"6179"}]},"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"full_name":"Krüger, Torben H","last_name":"Krüger","first_name":"Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Schröder","first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"volume":1,"date_created":"2019-03-28T10:21:17Z","date_updated":"2023-09-07T12:54:12Z","ec_funded":1},{"doi":"10.4171/jst/267","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1701.02956"}],"oa":1,"external_id":{"isi":["000484709400006"],"arxiv":["1701.02956"]},"quality_controlled":"1","isi":1,"month":"03","publication_identifier":{"issn":["1664-039X"]},"author":[{"id":"317CB464-F248-11E8-B48F-1D18A9856A87","first_name":"Adrian M","last_name":"Dietlein","full_name":"Dietlein, Adrian M"},{"full_name":"Gebert, Martin","first_name":"Martin","last_name":"Gebert"},{"last_name":"Müller","first_name":"Peter","full_name":"Müller, Peter"}],"date_updated":"2023-09-08T11:35:31Z","date_created":"2022-03-18T12:36:42Z","volume":9,"acknowledgement":"M.G. was supported by the DFG under grant GE 2871/1-1.","year":"2019","publication_status":"published","publisher":"European Mathematical Society Publishing House","department":[{"_id":"LaEr"}],"date_published":"2019-03-01T00:00:00Z","publication":"Journal of Spectral Theory","citation":{"chicago":"Dietlein, Adrian M, Martin Gebert, and Peter Müller. “Perturbations of Continuum Random Schrödinger Operators with Applications to Anderson Orthogonality and the Spectral Shift Function.” Journal of Spectral Theory. European Mathematical Society Publishing House, 2019. https://doi.org/10.4171/jst/267.","mla":"Dietlein, Adrian M., et al. “Perturbations of Continuum Random Schrödinger Operators with Applications to Anderson Orthogonality and the Spectral Shift Function.” Journal of Spectral Theory, vol. 9, no. 3, European Mathematical Society Publishing House, 2019, pp. 921–65, doi:10.4171/jst/267.","short":"A.M. Dietlein, M. Gebert, P. Müller, Journal of Spectral Theory 9 (2019) 921–965.","ista":"Dietlein AM, Gebert M, Müller P. 2019. Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function. Journal of Spectral Theory. 9(3), 921–965.","apa":"Dietlein, A. M., Gebert, M., & Müller, P. (2019). Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function. Journal of Spectral Theory. European Mathematical Society Publishing House. https://doi.org/10.4171/jst/267","ieee":"A. M. Dietlein, M. Gebert, and P. Müller, “Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function,” Journal of Spectral Theory, vol. 9, no. 3. European Mathematical Society Publishing House, pp. 921–965, 2019.","ama":"Dietlein AM, Gebert M, Müller P. Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function. Journal of Spectral Theory. 2019;9(3):921-965. doi:10.4171/jst/267"},"article_type":"original","page":"921-965","day":"01","article_processing_charge":"No","scopus_import":"1","keyword":["Random Schrödinger operators","spectral shift function","Anderson orthogonality"],"oa_version":"Preprint","_id":"10879","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","title":"Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function","status":"public","intvolume":" 9","abstract":[{"lang":"eng","text":"We study effects of a bounded and compactly supported perturbation on multidimensional continuum random Schrödinger operators in the region of complete localisation. Our main emphasis is on Anderson orthogonality for random Schrödinger operators. Among others, we prove that Anderson orthogonality does occur for Fermi energies in the region of complete localisation with a non-zero probability. This partially confirms recent non-rigorous findings [V. Khemani et al., Nature Phys. 11 (2015), 560–565]. The spectral shift function plays an important role in our analysis of Anderson orthogonality. We identify it with the index of the corresponding pair of spectral projections and explore the consequences thereof. All our results rely on the main technical estimate of this paper which guarantees separate exponential decay of the disorder-averaged Schatten p-norm of χa(f(H)−f(Hτ))χb in a and b. Here, Hτ is a perturbation of the random Schrödinger operator H, χa is the multiplication operator corresponding to the indicator function of a unit cube centred about a∈Rd, and f is in a suitable class of functions of bounded variation with distributional derivative supported in the region of complete localisation for H."}],"issue":"3","type":"journal_article"},{"date_published":"2019-09-25T00:00:00Z","publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","citation":{"chicago":"Ferrari, Patrick, Promit Ghosal, and Peter Nejjar. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics, 2019. https://doi.org/10.1214/18-AIHP916.","short":"P. Ferrari, P. Ghosal, P. Nejjar, Annales de l’institut Henri Poincare (B) Probability and Statistics 55 (2019) 1203–1225.","mla":"Ferrari, Patrick, et al. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 55, no. 3, Institute of Mathematical Statistics, 2019, pp. 1203–25, doi:10.1214/18-AIHP916.","ieee":"P. Ferrari, P. Ghosal, and P. Nejjar, “Limit law of a second class particle in TASEP with non-random initial condition,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 55, no. 3. Institute of Mathematical Statistics, pp. 1203–1225, 2019.","apa":"Ferrari, P., Ghosal, P., & Nejjar, P. (2019). Limit law of a second class particle in TASEP with non-random initial condition. Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/18-AIHP916","ista":"Ferrari P, Ghosal P, Nejjar P. 2019. Limit law of a second class particle in TASEP with non-random initial condition. Annales de l’institut Henri Poincare (B) Probability and Statistics. 55(3), 1203–1225.","ama":"Ferrari P, Ghosal P, Nejjar P. Limit law of a second class particle in TASEP with non-random initial condition. Annales de l’institut Henri Poincare (B) Probability and Statistics. 2019;55(3):1203-1225. doi:10.1214/18-AIHP916"},"article_type":"original","page":"1203-1225","day":"25","article_processing_charge":"No","scopus_import":"1","oa_version":"Preprint","_id":"72","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Limit law of a second class particle in TASEP with non-random initial condition","status":"public","intvolume":" 55","abstract":[{"lang":"eng","text":"We consider the totally asymmetric simple exclusion process (TASEP) with non-random initial condition having density ρ on ℤ− and λ on ℤ+, and a second class particle initially at the origin. For ρ<λ, there is a shock and the second class particle moves with speed 1−λ−ρ. For large time t, we show that the position of the second class particle fluctuates on a t1/3 scale and determine its limiting law. We also obtain the limiting distribution of the number of steps made by the second class particle until time t."}],"issue":"3","type":"journal_article","doi":"10.1214/18-AIHP916","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1710.02323","open_access":"1"}],"external_id":{"arxiv":["1710.02323"],"isi":["000487763200001"]},"isi":1,"quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"},{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"month":"09","publication_identifier":{"issn":["0246-0203"]},"author":[{"full_name":"Ferrari, Patrick","first_name":"Patrick","last_name":"Ferrari"},{"full_name":"Ghosal, Promit","first_name":"Promit","last_name":"Ghosal"},{"full_name":"Nejjar, Peter","last_name":"Nejjar","first_name":"Peter","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2018-12-11T11:44:29Z","date_updated":"2023-10-17T08:53:45Z","volume":55,"year":"2019","publication_status":"published","publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"ec_funded":1},{"publication_identifier":{"issn":["0246-0203"]},"month":"05","doi":"10.1214/18-AIHP894","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1706.08343"}],"external_id":{"arxiv":["1706.08343"],"isi":["000467793600003"]},"project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"quality_controlled":"1","isi":1,"ec_funded":1,"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"149"}]},"author":[{"full_name":"Alt, Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","last_name":"Alt","first_name":"Johannes"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","last_name":"Krüger","first_name":"Torben H","full_name":"Krüger, Torben H"},{"first_name":"Yuriy","last_name":"Nemish","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-7327-856X","full_name":"Nemish, Yuriy"}],"volume":55,"date_created":"2019-04-08T14:05:04Z","date_updated":"2023-10-17T12:20:20Z","year":"2019","department":[{"_id":"LaEr"}],"publisher":"Institut Henri Poincaré","publication_status":"published","article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2019-05-01T00:00:00Z","citation":{"ista":"Alt J, Erdös L, Krüger TH, Nemish Y. 2019. Location of the spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare. 55(2), 661–696.","ieee":"J. Alt, L. Erdös, T. H. Krüger, and Y. Nemish, “Location of the spectrum of Kronecker random matrices,” Annales de l’institut Henri Poincare, vol. 55, no. 2. Institut Henri Poincaré, pp. 661–696, 2019.","apa":"Alt, J., Erdös, L., Krüger, T. H., & Nemish, Y. (2019). Location of the spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare. Institut Henri Poincaré. https://doi.org/10.1214/18-AIHP894","ama":"Alt J, Erdös L, Krüger TH, Nemish Y. Location of the spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare. 2019;55(2):661-696. doi:10.1214/18-AIHP894","chicago":"Alt, Johannes, László Erdös, Torben H Krüger, and Yuriy Nemish. “Location of the Spectrum of Kronecker Random Matrices.” Annales de l’institut Henri Poincare. Institut Henri Poincaré, 2019. https://doi.org/10.1214/18-AIHP894.","mla":"Alt, Johannes, et al. “Location of the Spectrum of Kronecker Random Matrices.” Annales de l’institut Henri Poincare, vol. 55, no. 2, Institut Henri Poincaré, 2019, pp. 661–96, doi:10.1214/18-AIHP894.","short":"J. Alt, L. Erdös, T.H. Krüger, Y. Nemish, Annales de l’institut Henri Poincare 55 (2019) 661–696."},"publication":"Annales de l'institut Henri Poincare","page":"661-696","issue":"2","abstract":[{"lang":"eng","text":"For a general class of large non-Hermitian random block matrices X we prove that there are no eigenvalues away from a deterministic set with very high probability. This set is obtained from the Dyson equation of the Hermitization of X as the self-consistent approximation of the pseudospectrum. We demonstrate that the analysis of the matrix Dyson equation from (Probab. Theory Related Fields (2018)) offers a unified treatment of many structured matrix ensembles."}],"type":"journal_article","oa_version":"Preprint","_id":"6240","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 55","status":"public","title":"Location of the spectrum of Kronecker random matrices"},{"page":"375","citation":{"chicago":"Schröder, Dominik J. “From Dyson to Pearcey: Universal Statistics in Random Matrix Theory.” Institute of Science and Technology Austria, 2019. https://doi.org/10.15479/AT:ISTA:th6179.","mla":"Schröder, Dominik J. From Dyson to Pearcey: Universal Statistics in Random Matrix Theory. Institute of Science and Technology Austria, 2019, doi:10.15479/AT:ISTA:th6179.","short":"D.J. Schröder, From Dyson to Pearcey: Universal Statistics in Random Matrix Theory, Institute of Science and Technology Austria, 2019.","ista":"Schröder DJ. 2019. From Dyson to Pearcey: Universal statistics in random matrix theory. Institute of Science and Technology Austria.","ieee":"D. J. Schröder, “From Dyson to Pearcey: Universal statistics in random matrix theory,” Institute of Science and Technology Austria, 2019.","apa":"Schröder, D. J. (2019). From Dyson to Pearcey: Universal statistics in random matrix theory. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th6179","ama":"Schröder DJ. From Dyson to Pearcey: Universal statistics in random matrix theory. 2019. doi:10.15479/AT:ISTA:th6179"},"date_published":"2019-03-18T00:00:00Z","article_processing_charge":"No","has_accepted_license":"1","day":"18","title":"From Dyson to Pearcey: Universal statistics in random matrix theory","ddc":["515","519"],"status":"public","_id":"6179","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","file":[{"checksum":"6926f66f28079a81c4937e3764be00fc","date_updated":"2020-07-14T12:47:21Z","date_created":"2019-03-28T08:53:52Z","relation":"source_file","file_id":"6180","content_type":"application/x-gzip","file_size":7104482,"creator":"dernst","access_level":"closed","file_name":"2019_Schroeder_Thesis.tar.gz"},{"relation":"main_file","file_id":"6181","checksum":"7d0ebb8d1207e89768cdd497a5bf80fb","date_updated":"2020-07-14T12:47:21Z","date_created":"2019-03-28T08:53:52Z","access_level":"open_access","file_name":"2019_Schroeder_Thesis.pdf","content_type":"application/pdf","file_size":4228794,"creator":"dernst"}],"oa_version":"Published Version","alternative_title":["ISTA Thesis"],"type":"dissertation","abstract":[{"text":"In the first part of this thesis we consider large random matrices with arbitrary expectation and a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent in the bulk and edge regime. The main novel tool is a systematic diagrammatic control of a multivariate cumulant expansion.\r\nIn the second part we consider Wigner-type matrices and show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are uni- versal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner- Dyson-Mehta universality conjecture for the last remaining universality type. Our analysis holds not only for exact cusps, but approximate cusps as well, where an ex- tended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp, and extend the fast relaxation to equilibrium of the Dyson Brow- nian motion to the cusp regime.\r\nIn the third and final part we explore the entrywise linear statistics of Wigner ma- trices and identify the fluctuations for a large class of test functions with little regularity. This enables us to study the rectangular Young diagram obtained from the interlacing eigenvalues of the random matrix and its minor, and we find that, despite having the same limit, the fluctuations differ from those of the algebraic Young tableaux equipped with the Plancharel measure.","lang":"eng"}],"project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"oa":1,"language":[{"iso":"eng"}],"supervisor":[{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"}],"degree_awarded":"PhD","doi":"10.15479/AT:ISTA:th6179","publication_identifier":{"issn":["2663-337X"]},"month":"03","publisher":"Institute of Science and Technology Austria","department":[{"_id":"LaEr"}],"publication_status":"published","year":"2019","date_updated":"2024-02-22T14:34:33Z","date_created":"2019-03-28T08:58:59Z","related_material":{"record":[{"id":"1144","status":"public","relation":"part_of_dissertation"},{"status":"public","relation":"part_of_dissertation","id":"6186"},{"id":"6185","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"6182"},{"id":"1012","status":"public","relation":"part_of_dissertation"},{"status":"public","relation":"part_of_dissertation","id":"6184"}]},"author":[{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","first_name":"Dominik J"}],"ec_funded":1,"file_date_updated":"2020-07-14T12:47:21Z"},{"citation":{"mla":"Lee, Jii, and Kevin Schnelli. “Local Law and Tracy–Widom Limit for Sparse Random Matrices.” Probability Theory and Related Fields, vol. 171, no. 1–2, 543–616, Springer, 2018, doi:10.1007/s00440-017-0787-8.","short":"J. Lee, K. Schnelli, Probability Theory and Related Fields 171 (2018).","chicago":"Lee, Jii, and Kevin Schnelli. “Local Law and Tracy–Widom Limit for Sparse Random Matrices.” Probability Theory and Related Fields. Springer, 2018. https://doi.org/10.1007/s00440-017-0787-8.","ama":"Lee J, Schnelli K. Local law and Tracy–Widom limit for sparse random matrices. Probability Theory and Related Fields. 2018;171(1-2). doi:10.1007/s00440-017-0787-8","ista":"Lee J, Schnelli K. 2018. Local law and Tracy–Widom limit for sparse random matrices. Probability Theory and Related Fields. 171(1–2), 543–616.","apa":"Lee, J., & Schnelli, K. (2018). Local law and Tracy–Widom limit for sparse random matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-017-0787-8","ieee":"J. Lee and K. Schnelli, “Local law and Tracy–Widom limit for sparse random matrices,” Probability Theory and Related Fields, vol. 171, no. 1–2. Springer, 2018."},"publication":"Probability Theory and Related Fields","date_published":"2018-06-14T00:00:00Z","scopus_import":1,"day":"14","intvolume":" 171","status":"public","title":"Local law and Tracy–Widom limit for sparse random matrices","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"690","oa_version":"Preprint","type":"journal_article","issue":"1-2","abstract":[{"lang":"eng","text":"We consider spectral properties and the edge universality of sparse random matrices, the class of random matrices that includes the adjacency matrices of the Erdős–Rényi graph model G(N, p). We prove a local law for the eigenvalue density up to the spectral edges. Under a suitable condition on the sparsity, we also prove that the rescaled extremal eigenvalues exhibit GOE Tracy–Widom fluctuations if a deterministic shift of the spectral edge due to the sparsity is included. For the adjacency matrix of the Erdős–Rényi graph this establishes the Tracy–Widom fluctuations of the second largest eigenvalue when p is much larger than N−2/3 with a deterministic shift of order (Np)−1."}],"project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1605.08767"}],"oa":1,"external_id":{"arxiv":["1605.08767"]},"language":[{"iso":"eng"}],"doi":"10.1007/s00440-017-0787-8","month":"06","publisher":"Springer","department":[{"_id":"LaEr"}],"publication_status":"published","year":"2018","volume":171,"date_updated":"2021-01-12T08:09:33Z","date_created":"2018-12-11T11:47:56Z","author":[{"first_name":"Jii","last_name":"Lee","full_name":"Lee, Jii"},{"full_name":"Schnelli, Kevin","orcid":"0000-0003-0954-3231","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","last_name":"Schnelli","first_name":"Kevin"}],"article_number":"543-616","ec_funded":1,"publist_id":"7017"},{"oa_version":"Preprint","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"566","status":"public","title":"Local inhomogeneous circular law","intvolume":" 28","abstract":[{"text":"We consider large random matrices X with centered, independent entries which have comparable but not necessarily identical variances. Girko's circular law asserts that the spectrum is supported in a disk and in case of identical variances, the limiting density is uniform. In this special case, the local circular law by Bourgade et. al. [11,12] shows that the empirical density converges even locally on scales slightly above the typical eigenvalue spacing. In the general case, the limiting density is typically inhomogeneous and it is obtained via solving a system of deterministic equations. Our main result is the local inhomogeneous circular law in the bulk spectrum on the optimal scale for a general variance profile of the entries of X. \r\n\r\n","lang":"eng"}],"issue":"1","type":"journal_article","date_published":"2018-03-03T00:00:00Z","publication":"Annals Applied Probability ","citation":{"chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “Local Inhomogeneous Circular Law.” Annals Applied Probability . Institute of Mathematical Statistics, 2018. https://doi.org/10.1214/17-AAP1302.","short":"J. Alt, L. Erdös, T.H. Krüger, Annals Applied Probability 28 (2018) 148–203.","mla":"Alt, Johannes, et al. “Local Inhomogeneous Circular Law.” Annals Applied Probability , vol. 28, no. 1, Institute of Mathematical Statistics, 2018, pp. 148–203, doi:10.1214/17-AAP1302.","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “Local inhomogeneous circular law,” Annals Applied Probability , vol. 28, no. 1. Institute of Mathematical Statistics, pp. 148–203, 2018.","apa":"Alt, J., Erdös, L., & Krüger, T. H. (2018). Local inhomogeneous circular law. Annals Applied Probability . Institute of Mathematical Statistics. https://doi.org/10.1214/17-AAP1302","ista":"Alt J, Erdös L, Krüger TH. 2018. Local inhomogeneous circular law. Annals Applied Probability . 28(1), 148–203.","ama":"Alt J, Erdös L, Krüger TH. Local inhomogeneous circular law. Annals Applied Probability . 2018;28(1):148-203. doi:10.1214/17-AAP1302"},"article_type":"original","page":"148-203","day":"03","article_processing_charge":"No","scopus_import":"1","author":[{"id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","first_name":"Johannes","last_name":"Alt","full_name":"Alt, Johannes"},{"full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"full_name":"Krüger, Torben H","last_name":"Krüger","first_name":"Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87"}],"related_material":{"record":[{"id":"149","status":"public","relation":"dissertation_contains"}]},"date_updated":"2023-09-13T08:47:52Z","date_created":"2018-12-11T11:47:13Z","volume":28,"year":"2018","publication_status":"published","publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"ec_funded":1,"doi":"10.1214/17-AAP1302","language":[{"iso":"eng"}],"external_id":{"arxiv":["1612.07776 "],"isi":["000431721800005"]},"main_file_link":[{"url":"https://arxiv.org/abs/1612.07776 ","open_access":"1"}],"oa":1,"isi":1,"quality_controlled":"1","project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"month":"03"},{"_id":"181","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","title":"Power law decay for systems of randomly coupled differential equations","intvolume":" 50","oa_version":"Published Version","type":"journal_article","abstract":[{"lang":"eng","text":"We consider large random matrices X with centered, independent entries but possibly di erent variances. We compute the normalized trace of f(X)g(X∗) for f, g functions analytic on the spectrum of X. We use these results to compute the long time asymptotics for systems of coupled di erential equations with random coe cients. We show that when the coupling is critical, the norm squared of the solution decays like t−1/2."}],"issue":"3","publication":"SIAM Journal on Mathematical Analysis","citation":{"ama":"Erdös L, Krüger TH, Renfrew DT. Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. 2018;50(3):3271-3290. doi:10.1137/17M1143125","apa":"Erdös, L., Krüger, T. H., & Renfrew, D. T. (2018). Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/17M1143125","ieee":"L. Erdös, T. H. Krüger, and D. T. Renfrew, “Power law decay for systems of randomly coupled differential equations,” SIAM Journal on Mathematical Analysis, vol. 50, no. 3. Society for Industrial and Applied Mathematics , pp. 3271–3290, 2018.","ista":"Erdös L, Krüger TH, Renfrew DT. 2018. Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. 50(3), 3271–3290.","short":"L. Erdös, T.H. Krüger, D.T. Renfrew, SIAM Journal on Mathematical Analysis 50 (2018) 3271–3290.","mla":"Erdös, László, et al. “Power Law Decay for Systems of Randomly Coupled Differential Equations.” SIAM Journal on Mathematical Analysis, vol. 50, no. 3, Society for Industrial and Applied Mathematics , 2018, pp. 3271–90, doi:10.1137/17M1143125.","chicago":"Erdös, László, Torben H Krüger, and David T Renfrew. “Power Law Decay for Systems of Randomly Coupled Differential Equations.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/17M1143125."},"page":"3271 - 3290","date_published":"2018-01-01T00:00:00Z","scopus_import":"1","day":"01","article_processing_charge":"No","year":"2018","acknowledgement":"The work of the second author was also partially supported by the Hausdorff Center of Mathematics.","publication_status":"published","publisher":"Society for Industrial and Applied Mathematics ","department":[{"_id":"LaEr"}],"author":[{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Krüger, Torben H","last_name":"Krüger","first_name":"Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Renfrew, David T","last_name":"Renfrew","first_name":"David T","orcid":"0000-0003-3493-121X","id":"4845BF6A-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2018-12-11T11:45:03Z","date_updated":"2023-09-15T12:05:52Z","volume":50,"publist_id":"7740","ec_funded":1,"external_id":{"isi":["000437018500032"],"arxiv":["1708.01546"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.01546"}],"oa":1,"quality_controlled":"1","isi":1,"project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"},{"_id":"258F40A4-B435-11E9-9278-68D0E5697425","grant_number":"M02080","name":"Structured Non-Hermitian Random Matrices","call_identifier":"FWF"}],"doi":"10.1137/17M1143125","language":[{"iso":"eng"}],"month":"01"},{"type":"journal_article","abstract":[{"lang":"eng","text":"We consider a Wigner-type ensemble, i.e. large hermitian N×N random matrices H=H∗ with centered independent entries and with a general matrix of variances Sxy=𝔼∣∣Hxy∣∣2. The norm of H is asymptotically given by the maximum of the support of the self-consistent density of states. We establish a bound on this maximum in terms of norms of powers of S that substantially improves the earlier bound 2∥S∥1/2∞ given in [O. Ajanki, L. Erdős and T. Krüger, Universality for general Wigner-type matrices, Prob. Theor. Rel. Fields169 (2017) 667–727]. The key element of the proof is an effective Markov chain approximation for the contributions of the weighted Dyck paths appearing in the iterative solution of the corresponding Dyson equation."}],"status":"public","title":"Bounds on the norm of Wigner-type random matrices","_id":"5971","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Preprint","scopus_import":"1","article_processing_charge":"No","day":"26","citation":{"ieee":"L. Erdös and P. Mühlbacher, “Bounds on the norm of Wigner-type random matrices,” Random matrices: Theory and applications. World Scientific Publishing, 2018.","apa":"Erdös, L., & Mühlbacher, P. (2018). Bounds on the norm of Wigner-type random matrices. Random Matrices: Theory and Applications. World Scientific Publishing. https://doi.org/10.1142/s2010326319500096","ista":"Erdös L, Mühlbacher P. 2018. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications., 1950009.","ama":"Erdös L, Mühlbacher P. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications. 2018. doi:10.1142/s2010326319500096","chicago":"Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random Matrices.” Random Matrices: Theory and Applications. World Scientific Publishing, 2018. https://doi.org/10.1142/s2010326319500096.","short":"L. Erdös, P. Mühlbacher, Random Matrices: Theory and Applications (2018).","mla":"Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random Matrices.” Random Matrices: Theory and Applications, 1950009, World Scientific Publishing, 2018, doi:10.1142/s2010326319500096."},"publication":"Random matrices: Theory and applications","date_published":"2018-09-26T00:00:00Z","article_number":"1950009","ec_funded":1,"department":[{"_id":"LaEr"}],"publisher":"World Scientific Publishing","publication_status":"published","year":"2018","date_created":"2019-02-13T10:40:54Z","date_updated":"2023-09-19T14:24:05Z","author":[{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Peter","last_name":"Mühlbacher","full_name":"Mühlbacher, Peter"}],"publication_identifier":{"issn":["2010-3263"],"eissn":["2010-3271"]},"month":"09","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"}],"isi":1,"quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/1802.05175","open_access":"1"}],"external_id":{"arxiv":["1802.05175"],"isi":["000477677200002"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1142/s2010326319500096"},{"type":"journal_article","issue":"10","abstract":[{"lang":"eng","text":"We prove a new central limit theorem (CLT) for the difference of linear eigenvalue statistics of a Wigner random matrix H and its minor H and find that the fluctuation is much smaller than the fluctuations of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of H and H. In particular, our theorem identifies the fluctuation of Kerov's rectangular Young diagrams, defined by the interlacing eigenvalues ofH and H, around their asymptotic shape, the Vershik'Kerov'Logan'Shepp curve. Young diagrams equipped with the Plancherel measure follow the same limiting shape. For this, algebraically motivated, ensemble a CLT has been obtained in Ivanov and Olshanski [20] which is structurally similar to our result but the variance is different, indicating that the analogy between the two models has its limitations. Moreover, our theorem shows that Borodin's result [7] on the convergence of the spectral distribution of Wigner matrices to a Gaussian free field also holds in derivative sense."}],"intvolume":" 2018","status":"public","title":"Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"1012","oa_version":"Preprint","scopus_import":"1","article_processing_charge":"No","day":"18","page":"3255-3298","citation":{"ieee":"L. Erdös and D. J. Schröder, “Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues,” International Mathematics Research Notices, vol. 2018, no. 10. Oxford University Press, pp. 3255–3298, 2018.","apa":"Erdös, L., & Schröder, D. J. (2018). Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnw330","ista":"Erdös L, Schröder DJ. 2018. Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. 2018(10), 3255–3298.","ama":"Erdös L, Schröder DJ. Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. 2018;2018(10):3255-3298. doi:10.1093/imrn/rnw330","chicago":"Erdös, László, and Dominik J Schröder. “Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues.” International Mathematics Research Notices. Oxford University Press, 2018. https://doi.org/10.1093/imrn/rnw330.","short":"L. Erdös, D.J. Schröder, International Mathematics Research Notices 2018 (2018) 3255–3298.","mla":"Erdös, László, and Dominik J. Schröder. “Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues.” International Mathematics Research Notices, vol. 2018, no. 10, Oxford University Press, 2018, pp. 3255–98, doi:10.1093/imrn/rnw330."},"publication":"International Mathematics Research Notices","date_published":"2018-05-18T00:00:00Z","ec_funded":1,"publist_id":"6383","department":[{"_id":"LaEr"}],"publisher":"Oxford University Press","publication_status":"published","year":"2018","volume":2018,"date_created":"2018-12-11T11:49:41Z","date_updated":"2023-09-22T09:44:21Z","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"6179"}]},"author":[{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"},{"first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"publication_identifier":{"issn":["10737928"]},"month":"05","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"isi":1,"quality_controlled":"1","oa":1,"external_id":{"arxiv":["1608.05163"],"isi":["000441668300009"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.05163"}],"language":[{"iso":"eng"}],"doi":"10.1093/imrn/rnw330"},{"issue":"2","abstract":[{"lang":"eng","text":"We consider the totally asymmetric simple exclusion process in a critical scaling parametrized by a≥0, which creates a shock in the particle density of order aT−1/3, T the observation time. When starting from step initial data, we provide bounds on the limiting law which in particular imply that in the double limit lima→∞limT→∞ one recovers the product limit law and the degeneration of the correlation length observed at shocks of order 1. This result is shown to apply to a general last-passage percolation model. We also obtain bounds on the two-point functions of several airy processes."}],"type":"journal_article","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"5981","checksum":"2ded46aa284a836a8cbb34133a64f1cb","date_updated":"2020-07-14T12:47:46Z","date_created":"2019-02-14T09:44:10Z","access_level":"open_access","file_name":"2018_ALEA_Nejjar.pdf","content_type":"application/pdf","file_size":394851,"creator":"kschuh"}],"_id":"70","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 15","title":"Transition to shocks in TASEP and decoupling of last passage times","ddc":["510"],"status":"public","article_processing_charge":"No","has_accepted_license":"1","day":"01","scopus_import":"1","date_published":"2018-10-01T00:00:00Z","citation":{"chicago":"Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” Latin American Journal of Probability and Mathematical Statistics. Instituto Nacional de Matematica Pura e Aplicada, 2018. https://doi.org/10.30757/ALEA.v15-49.","mla":"Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” Latin American Journal of Probability and Mathematical Statistics, vol. 15, no. 2, Instituto Nacional de Matematica Pura e Aplicada, 2018, pp. 1311–34, doi:10.30757/ALEA.v15-49.","short":"P. Nejjar, Latin American Journal of Probability and Mathematical Statistics 15 (2018) 1311–1334.","ista":"Nejjar P. 2018. Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. 15(2), 1311–1334.","ieee":"P. Nejjar, “Transition to shocks in TASEP and decoupling of last passage times,” Latin American Journal of Probability and Mathematical Statistics, vol. 15, no. 2. Instituto Nacional de Matematica Pura e Aplicada, pp. 1311–1334, 2018.","apa":"Nejjar, P. (2018). Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. Instituto Nacional de Matematica Pura e Aplicada. https://doi.org/10.30757/ALEA.v15-49","ama":"Nejjar P. Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. 2018;15(2):1311-1334. doi:10.30757/ALEA.v15-49"},"publication":"Latin American Journal of Probability and Mathematical Statistics","page":"1311-1334","article_type":"original","ec_funded":1,"file_date_updated":"2020-07-14T12:47:46Z","author":[{"first_name":"Peter","last_name":"Nejjar","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","full_name":"Nejjar, Peter"}],"volume":15,"date_updated":"2023-10-10T13:11:29Z","date_created":"2018-12-11T11:44:28Z","year":"2018","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"publisher":"Instituto Nacional de Matematica Pura e Aplicada","publication_status":"published","publication_identifier":{"issn":["1980-0436"]},"month":"10","doi":"10.30757/ALEA.v15-49","language":[{"iso":"eng"}],"oa":1,"external_id":{"arxiv":["1705.08836"],"isi":["000460475800022"]},"project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"},{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"isi":1,"quality_controlled":"1"},{"doi":"10.14232/actasm-018-753-y","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1802.03305","open_access":"1"}],"oa":1,"external_id":{"arxiv":["1802.03305"]},"project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"quality_controlled":"1","publication_identifier":{"eissn":["2064-8316"],"issn":["0001-6969"]},"month":"06","author":[{"full_name":"Virosztek, Daniel","first_name":"Daniel","last_name":"Virosztek","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-1109-5511"}],"volume":84,"date_updated":"2023-10-16T10:29:22Z","date_created":"2018-12-11T11:45:36Z","acknowledgement":"The author was supported by the ISTFELLOW program of the Institute of Science and Technol- ogy Austria (project code IC1027FELL01) and partially supported by the Hungarian National Research, Development and Innovation Office, NKFIH (grant no. K124152).","year":"2018","department":[{"_id":"LaEr"}],"publisher":"Springer Nature","publication_status":"published","publist_id":"7615","ec_funded":1,"date_published":"2018-06-04T00:00:00Z","citation":{"chicago":"Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances - a Survey and Some New Results.” Acta Scientiarum Mathematicarum. Springer Nature, 2018. https://doi.org/10.14232/actasm-018-753-y.","mla":"Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances - a Survey and Some New Results.” Acta Scientiarum Mathematicarum, vol. 84, no. 1–2, Springer Nature, 2018, pp. 65–80, doi:10.14232/actasm-018-753-y.","short":"D. Virosztek, Acta Scientiarum Mathematicarum 84 (2018) 65–80.","ista":"Virosztek D. 2018. Maps on probability measures preserving certain distances - a survey and some new results. Acta Scientiarum Mathematicarum. 84(1–2), 65–80.","ieee":"D. Virosztek, “Maps on probability measures preserving certain distances - a survey and some new results,” Acta Scientiarum Mathematicarum, vol. 84, no. 1–2. Springer Nature, pp. 65–80, 2018.","apa":"Virosztek, D. (2018). Maps on probability measures preserving certain distances - a survey and some new results. Acta Scientiarum Mathematicarum. Springer Nature. https://doi.org/10.14232/actasm-018-753-y","ama":"Virosztek D. Maps on probability measures preserving certain distances - a survey and some new results. Acta Scientiarum Mathematicarum. 2018;84(1-2):65-80. doi:10.14232/actasm-018-753-y"},"publication":"Acta Scientiarum Mathematicarum","page":"65 - 80","article_type":"original","article_processing_charge":"No","day":"04","scopus_import":"1","oa_version":"Preprint","_id":"284","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 84","status":"public","title":"Maps on probability measures preserving certain distances - a survey and some new results","issue":"1-2","abstract":[{"lang":"eng","text":"Borel probability measures living on metric spaces are fundamental\r\nmathematical objects. There are several meaningful distance functions that make the collection of the probability measures living on a certain space a metric space. We are interested in the description of the structure of the isometries of such metric spaces. We overview some of the recent results of the topic and we also provide some new ones concerning the Wasserstein distance. More specifically, we consider the space of all Borel probability measures on the unit sphere of a Euclidean space endowed with the Wasserstein metric W_p for arbitrary p >= 1, and we show that the action of a Wasserstein isometry on the set of Dirac measures is induced by an isometry of the underlying unit sphere."}],"type":"journal_article"},{"date_updated":"2023-12-18T10:46:08Z","date_created":"2019-03-28T09:20:06Z","oa_version":"Preprint","author":[{"id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","last_name":"Alt","first_name":"Johannes","full_name":"Alt, Johannes"},{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"last_name":"Krüger","first_name":"Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H"}],"related_material":{"record":[{"id":"149","relation":"dissertation_contains","status":"public"},{"relation":"later_version","status":"public","id":"14694"}]},"status":"public","title":"The Dyson equation with linear self-energy: Spectral bands, edges and cusps","publication_status":"submitted","department":[{"_id":"LaEr"}],"year":"2018","_id":"6183","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"We study the unique solution $m$ of the Dyson equation \\[ -m(z)^{-1} = z - a\r\n+ S[m(z)] \\] on a von Neumann algebra $\\mathcal{A}$ with the constraint\r\n$\\mathrm{Im}\\,m\\geq 0$. Here, $z$ lies in the complex upper half-plane, $a$ is\r\na self-adjoint element of $\\mathcal{A}$ and $S$ is a positivity-preserving\r\nlinear operator on $\\mathcal{A}$. We show that $m$ is the Stieltjes transform\r\nof a compactly supported $\\mathcal{A}$-valued measure on $\\mathbb{R}$. Under\r\nsuitable assumptions, we establish that this measure has a uniformly\r\n$1/3$-H\\\"{o}lder continuous density with respect to the Lebesgue measure, which\r\nis supported on finitely many intervals, called bands. In fact, the density is\r\nanalytic inside the bands with a square-root growth at the edges and internal\r\ncubic root cusps whenever the gap between two bands vanishes. The shape of\r\nthese singularities is universal and no other singularity may occur. We give a\r\nprecise asymptotic description of $m$ near the singular points. These\r\nasymptotics generalize the analysis at the regular edges given in the companion\r\npaper on the Tracy-Widom universality for the edge eigenvalue statistics for\r\ncorrelated random matrices [arXiv:1804.07744] and they play a key role in the\r\nproof of the Pearcey universality at the cusp for Wigner-type matrices\r\n[arXiv:1809.03971,arXiv:1811.04055]. We also extend the finite dimensional band\r\nmass formula from [arXiv:1804.07744] to the von Neumann algebra setting by\r\nshowing that the spectral mass of the bands is topologically rigid under\r\ndeformations and we conclude that these masses are quantized in some important\r\ncases.","lang":"eng"}],"article_number":"1804.07752","type":"preprint","language":[{"iso":"eng"}],"date_published":"2018-04-20T00:00:00Z","publication":"arXiv","oa":1,"citation":{"ama":"Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. arXiv.","ista":"Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. arXiv, 1804.07752.","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy: Spectral bands, edges and cusps,” arXiv. .","apa":"Alt, J., Erdös, L., & Krüger, T. H. (n.d.). The Dyson equation with linear self-energy: Spectral bands, edges and cusps. arXiv.","mla":"Alt, Johannes, et al. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” ArXiv, 1804.07752.","short":"J. Alt, L. Erdös, T.H. Krüger, ArXiv (n.d.).","chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” ArXiv, n.d."},"main_file_link":[{"url":"https://arxiv.org/abs/1804.07752","open_access":"1"}],"external_id":{"arxiv":["1804.07752"]},"day":"20","month":"04","article_processing_charge":"No"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"556","intvolume":" 19","title":"The free boundary Schur process and applications I","status":"public","ddc":["500"],"oa_version":"Published Version","file":[{"file_name":"2018_Annales_Betea.pdf","access_level":"open_access","content_type":"application/pdf","file_size":3084674,"creator":"dernst","relation":"main_file","file_id":"5866","date_updated":"2020-07-14T12:47:03Z","date_created":"2019-01-21T15:18:55Z","checksum":"0c38abe73569b7166b7487ad5d23cc68"}],"type":"journal_article","issue":"12","abstract":[{"text":"We investigate the free boundary Schur process, a variant of the Schur process introduced by Okounkov and Reshetikhin, where we allow the first and the last partitions to be arbitrary (instead of empty in the original setting). The pfaffian Schur process, previously studied by several authors, is recovered when just one of the boundary partitions is left free. We compute the correlation functions of the process in all generality via the free fermion formalism, which we extend with the thorough treatment of “free boundary states.” For the case of one free boundary, our approach yields a new proof that the process is pfaffian. For the case of two free boundaries, we find that the process is not pfaffian, but a closely related process is. We also study three different applications of the Schur process with one free boundary: fluctuations of symmetrized last passage percolation models, limit shapes and processes for symmetric plane partitions and for plane overpartitions.","lang":"eng"}],"citation":{"ama":"Betea D, Bouttier J, Nejjar P, Vuletic M. The free boundary Schur process and applications I. Annales Henri Poincare. 2018;19(12):3663-3742. doi:10.1007/s00023-018-0723-1","apa":"Betea, D., Bouttier, J., Nejjar, P., & Vuletic, M. (2018). The free boundary Schur process and applications I. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-018-0723-1","ieee":"D. Betea, J. Bouttier, P. Nejjar, and M. Vuletic, “The free boundary Schur process and applications I,” Annales Henri Poincare, vol. 19, no. 12. Springer Nature, pp. 3663–3742, 2018.","ista":"Betea D, Bouttier J, Nejjar P, Vuletic M. 2018. The free boundary Schur process and applications I. Annales Henri Poincare. 19(12), 3663–3742.","short":"D. Betea, J. Bouttier, P. Nejjar, M. Vuletic, Annales Henri Poincare 19 (2018) 3663–3742.","mla":"Betea, Dan, et al. “The Free Boundary Schur Process and Applications I.” Annales Henri Poincare, vol. 19, no. 12, Springer Nature, 2018, pp. 3663–742, doi:10.1007/s00023-018-0723-1.","chicago":"Betea, Dan, Jeremie Bouttier, Peter Nejjar, and Mirjana Vuletic. “The Free Boundary Schur Process and Applications I.” Annales Henri Poincare. Springer Nature, 2018. https://doi.org/10.1007/s00023-018-0723-1."},"publication":"Annales Henri Poincare","page":"3663-3742","article_type":"original","date_published":"2018-11-13T00:00:00Z","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"13","year":"2018","publisher":"Springer Nature","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"publication_status":"published","author":[{"full_name":"Betea, Dan","first_name":"Dan","last_name":"Betea"},{"full_name":"Bouttier, Jeremie","last_name":"Bouttier","first_name":"Jeremie"},{"full_name":"Nejjar, Peter","last_name":"Nejjar","first_name":"Peter","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Vuletic, Mirjana","first_name":"Mirjana","last_name":"Vuletic"}],"volume":19,"date_updated":"2024-02-20T10:48:17Z","date_created":"2018-12-11T11:47:09Z","publist_id":"7258","ec_funded":1,"file_date_updated":"2020-07-14T12:47:03Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"arxiv":["1704.05809"]},"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"},{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"}],"quality_controlled":"1","doi":"10.1007/s00023-018-0723-1","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1424-0637"]},"month":"11"},{"date_published":"2018-07-12T00:00:00Z","citation":{"chicago":"Alt, Johannes. “Dyson Equation and Eigenvalue Statistics of Random Matrices.” Institute of Science and Technology Austria, 2018. https://doi.org/10.15479/AT:ISTA:TH_1040.","short":"J. Alt, Dyson Equation and Eigenvalue Statistics of Random Matrices, Institute of Science and Technology Austria, 2018.","mla":"Alt, Johannes. Dyson Equation and Eigenvalue Statistics of Random Matrices. Institute of Science and Technology Austria, 2018, doi:10.15479/AT:ISTA:TH_1040.","apa":"Alt, J. (2018). Dyson equation and eigenvalue statistics of random matrices. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:TH_1040","ieee":"J. Alt, “Dyson equation and eigenvalue statistics of random matrices,” Institute of Science and Technology Austria, 2018.","ista":"Alt J. 2018. Dyson equation and eigenvalue statistics of random matrices. Institute of Science and Technology Austria.","ama":"Alt J. Dyson equation and eigenvalue statistics of random matrices. 2018. doi:10.15479/AT:ISTA:TH_1040"},"page":"456","article_processing_charge":"No","has_accepted_license":"1","day":"12","pubrep_id":"1040","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"6241","date_updated":"2020-07-14T12:44:57Z","date_created":"2019-04-08T13:55:20Z","checksum":"d4dad55a7513f345706aaaba90cb1bb8","file_name":"2018_thesis_Alt.pdf","access_level":"open_access","file_size":5801709,"content_type":"application/pdf","creator":"dernst"},{"file_name":"2018_thesis_Alt_source.zip","access_level":"closed","content_type":"application/zip","file_size":3802059,"creator":"dernst","relation":"source_file","file_id":"6242","date_created":"2019-04-08T13:55:20Z","date_updated":"2020-07-14T12:44:57Z","checksum":"d73fcf46300dce74c403f2b491148ab4"}],"_id":"149","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","ddc":["515","519"],"status":"public","title":"Dyson equation and eigenvalue statistics of random matrices","abstract":[{"text":"The eigenvalue density of many large random matrices is well approximated by a deterministic measure, the self-consistent density of states. In the present work, we show this behaviour for several classes of random matrices. In fact, we establish that, in each of these classes, the self-consistent density of states approximates the eigenvalue density of the random matrix on all scales slightly above the typical eigenvalue spacing. For large classes of random matrices, the self-consistent density of states exhibits several universal features. We prove that, under suitable assumptions, random Gram matrices and Hermitian random matrices with decaying correlations have a 1/3-Hölder continuous self-consistent density of states ρ on R, which is analytic, where it is positive, and has either a square root edge or a cubic root cusp, where it vanishes. We, thus, extend the validity of the corresponding result for Wigner-type matrices from [4, 5, 7]. We show that ρ is determined as the inverse Stieltjes transform of the normalized trace of the unique solution m(z) to the Dyson equation −m(z) −1 = z − a + S[m(z)] on C N×N with the constraint Im m(z) ≥ 0. Here, z lies in the complex upper half-plane, a is a self-adjoint element of C N×N and S is a positivity-preserving operator on C N×N encoding the first two moments of the random matrix. In order to analyze a possible limit of ρ for N → ∞ and address some applications in free probability theory, we also consider the Dyson equation on infinite dimensional von Neumann algebras. We present two applications to random matrices. We first establish that, under certain assumptions, large random matrices with independent entries have a rotationally symmetric self-consistent density of states which is supported on a centered disk in C. Moreover, it is infinitely often differentiable apart from a jump on the boundary of this disk. Second, we show edge universality at all regular (not necessarily extreme) spectral edges for Hermitian random matrices with decaying correlations.","lang":"eng"}],"type":"dissertation","alternative_title":["ISTA Thesis"],"doi":"10.15479/AT:ISTA:TH_1040","language":[{"iso":"eng"}],"degree_awarded":"PhD","supervisor":[{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"publication_identifier":{"issn":["2663-337X"]},"month":"07","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"1677"},{"id":"550","status":"public","relation":"part_of_dissertation"},{"status":"public","relation":"part_of_dissertation","id":"6183"},{"status":"public","relation":"part_of_dissertation","id":"566"},{"id":"1010","status":"public","relation":"part_of_dissertation"},{"status":"public","relation":"part_of_dissertation","id":"6240"},{"id":"6184","status":"public","relation":"part_of_dissertation"}]},"author":[{"full_name":"Alt, Johannes","first_name":"Johannes","last_name":"Alt","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2024-02-22T14:34:33Z","date_created":"2018-12-11T11:44:53Z","year":"2018","department":[{"_id":"LaEr"}],"publisher":"Institute of Science and Technology Austria","publication_status":"published","ec_funded":1,"publist_id":"7772","file_date_updated":"2020-07-14T12:44:57Z"},{"ec_funded":1,"publist_id":"7337","author":[{"last_name":"Bourgade","first_name":"Paul","full_name":"Bourgade, Paul"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"Erdös, László"},{"last_name":"Yau","first_name":"Horng","full_name":"Yau, Horng"},{"full_name":"Yin, Jun","first_name":"Jun","last_name":"Yin"}],"date_updated":"2021-01-12T08:00:57Z","date_created":"2018-12-11T11:46:43Z","volume":21,"year":"2017","publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"International Press","month":"08","publication_identifier":{"issn":["10950761"]},"doi":"10.4310/ATMP.2017.v21.n3.a5","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1602.02312"}],"quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"abstract":[{"text":"We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, W ~ N. All previous results concerning universality of non-Gaussian random matrices are for mean-field models. By relying on a new mean-field reduction technique, we deduce universality from quantum unique ergodicity for band matrices.","lang":"eng"}],"issue":"3","type":"journal_article","oa_version":"Submitted Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"483","status":"public","title":"Universality for a class of random band matrices","intvolume":" 21","day":"25","scopus_import":1,"date_published":"2017-08-25T00:00:00Z","publication":"Advances in Theoretical and Mathematical Physics","citation":{"mla":"Bourgade, Paul, et al. “Universality for a Class of Random Band Matrices.” Advances in Theoretical and Mathematical Physics, vol. 21, no. 3, International Press, 2017, pp. 739–800, doi:10.4310/ATMP.2017.v21.n3.a5.","short":"P. Bourgade, L. Erdös, H. Yau, J. Yin, Advances in Theoretical and Mathematical Physics 21 (2017) 739–800.","chicago":"Bourgade, Paul, László Erdös, Horng Yau, and Jun Yin. “Universality for a Class of Random Band Matrices.” Advances in Theoretical and Mathematical Physics. International Press, 2017. https://doi.org/10.4310/ATMP.2017.v21.n3.a5.","ama":"Bourgade P, Erdös L, Yau H, Yin J. Universality for a class of random band matrices. Advances in Theoretical and Mathematical Physics. 2017;21(3):739-800. doi:10.4310/ATMP.2017.v21.n3.a5","ista":"Bourgade P, Erdös L, Yau H, Yin J. 2017. Universality for a class of random band matrices. Advances in Theoretical and Mathematical Physics. 21(3), 739–800.","ieee":"P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Universality for a class of random band matrices,” Advances in Theoretical and Mathematical Physics, vol. 21, no. 3. International Press, pp. 739–800, 2017.","apa":"Bourgade, P., Erdös, L., Yau, H., & Yin, J. (2017). Universality for a class of random band matrices. Advances in Theoretical and Mathematical Physics. International Press. https://doi.org/10.4310/ATMP.2017.v21.n3.a5"},"page":"739 - 800"},{"date_created":"2018-12-11T11:47:13Z","date_updated":"2022-05-24T06:57:28Z","volume":28,"author":[{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"first_name":"Horng","last_name":"Yau","full_name":"Yau, Horng"}],"publication_status":"published","publisher":"American Mathematical Society","department":[{"_id":"LaEr"}],"year":"2017","publist_id":"7247","ec_funded":1,"language":[{"iso":"eng"}],"doi":"10.1090/cln/028","quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"month":"01","publication_identifier":{"isbn":["9-781-4704-3648-3"],"eisbn":["978-1-4704-4194-4"]},"oa_version":"None","status":"public","title":"A Dynamical Approach to Random Matrix Theory","intvolume":" 28","_id":"567","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","text":"This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality.\r\n"}],"alternative_title":["Courant Lecture Notes"],"type":"book","date_published":"2017-01-01T00:00:00Z","page":"226","citation":{"ama":"Erdös L, Yau H. A Dynamical Approach to Random Matrix Theory. Vol 28. American Mathematical Society; 2017. doi:10.1090/cln/028","ista":"Erdös L, Yau H. 2017. A Dynamical Approach to Random Matrix Theory, American Mathematical Society, 226p.","apa":"Erdös, L., & Yau, H. (2017). A Dynamical Approach to Random Matrix Theory (Vol. 28). American Mathematical Society. https://doi.org/10.1090/cln/028","ieee":"L. Erdös and H. Yau, A Dynamical Approach to Random Matrix Theory, vol. 28. American Mathematical Society, 2017.","mla":"Erdös, László, and Horng Yau. A Dynamical Approach to Random Matrix Theory. Vol. 28, American Mathematical Society, 2017, doi:10.1090/cln/028.","short":"L. Erdös, H. Yau, A Dynamical Approach to Random Matrix Theory, American Mathematical Society, 2017.","chicago":"Erdös, László, and Horng Yau. A Dynamical Approach to Random Matrix Theory. Vol. 28. Courant Lecture Notes. American Mathematical Society, 2017. https://doi.org/10.1090/cln/028."},"day":"01","article_processing_charge":"No","series_title":"Courant Lecture Notes"},{"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1504.00650"}],"project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"}],"quality_controlled":"1","doi":"10.1214/16-AIHP765","language":[{"iso":"eng"}],"publication_identifier":{"issn":["02460203"]},"month":"11","year":"2017","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","publication_status":"published","author":[{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0954-3231","first_name":"Kevin","last_name":"Schnelli","full_name":"Schnelli, Kevin"}],"volume":53,"date_updated":"2021-01-12T08:06:22Z","date_created":"2018-12-11T11:47:30Z","publist_id":"7189","ec_funded":1,"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","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.","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","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.","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.","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."},"publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","page":"1606 - 1656","date_published":"2017-11-01T00:00:00Z","scopus_import":1,"day":"01","_id":"615","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","intvolume":" 53","title":"Universality for random matrix flows with time dependent density","status":"public","oa_version":"Submitted Version","type":"journal_article","issue":"4","abstract":[{"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.","lang":"eng"}]},{"intvolume":" 70","status":"public","title":"Singularities of solutions to quadratic vector equations on the complex upper half plane","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"721","oa_version":"Submitted Version","type":"journal_article","issue":"9","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."}],"page":"1672 - 1705","citation":{"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.","ieee":"O. H. Ajanki, T. H. Krüger, and L. Erdös, “Singularities of solutions to quadratic vector equations on the complex upper half plane,” Communications on Pure and Applied Mathematics, vol. 70, no. 9. Wiley-Blackwell, pp. 1672–1705, 2017.","apa":"Ajanki, O. H., Krüger, T. H., & Erdös, L. (2017). Singularities of solutions to quadratic vector equations on the complex upper half plane. Communications on Pure and Applied Mathematics. Wiley-Blackwell. https://doi.org/10.1002/cpa.21639","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","chicago":"Ajanki, Oskari H, Torben H Krüger, and László Erdös. “Singularities of Solutions to Quadratic Vector Equations on the Complex Upper Half Plane.” Communications on Pure and Applied Mathematics. Wiley-Blackwell, 2017. https://doi.org/10.1002/cpa.21639.","mla":"Ajanki, Oskari H., et al. “Singularities of Solutions to Quadratic Vector Equations on the Complex Upper Half Plane.” Communications on Pure and Applied Mathematics, vol. 70, no. 9, Wiley-Blackwell, 2017, pp. 1672–705, doi:10.1002/cpa.21639.","short":"O.H. Ajanki, T.H. Krüger, L. Erdös, Communications on Pure and Applied Mathematics 70 (2017) 1672–1705."},"publication":"Communications on Pure and Applied Mathematics","date_published":"2017-09-01T00:00:00Z","scopus_import":1,"day":"01","publisher":"Wiley-Blackwell","department":[{"_id":"LaEr"}],"publication_status":"published","year":"2017","volume":70,"date_created":"2018-12-11T11:48:08Z","date_updated":"2021-01-12T08:12:24Z","author":[{"last_name":"Ajanki","first_name":"Oskari H","id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87","full_name":"Ajanki, Oskari H"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","first_name":"Torben H","last_name":"Krüger","full_name":"Krüger, Torben H"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","full_name":"Erdös, László"}],"ec_funded":1,"publist_id":"6959","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"}],"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1512.03703"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1002/cpa.21639","publication_identifier":{"issn":["00103640"]},"month":"09"},{"type":"journal_article","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."}],"intvolume":" 22","ddc":["539"],"title":"Singularities of the density of states of random Gram matrices","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"550","oa_version":"Published Version","file":[{"checksum":"0ec05303a0de190de145654237984c79","date_updated":"2020-07-14T12:47:00Z","date_created":"2018-12-12T10:08:04Z","relation":"main_file","file_id":"4663","content_type":"application/pdf","file_size":470876,"creator":"system","access_level":"open_access","file_name":"IST-2018-926-v1+1_euclid.ecp.1511233247.pdf"}],"pubrep_id":"926","scopus_import":1,"has_accepted_license":"1","day":"21","citation":{"ieee":"J. Alt, “Singularities of the density of states of random Gram matrices,” Electronic Communications in Probability, vol. 22. Institute of Mathematical Statistics, 2017.","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","ista":"Alt J. 2017. Singularities of the density of states of random Gram matrices. Electronic Communications in Probability. 22, 63.","ama":"Alt J. Singularities of the density of states of random Gram matrices. Electronic Communications in Probability. 2017;22. doi: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.","short":"J. Alt, Electronic Communications in Probability 22 (2017).","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."},"publication":"Electronic Communications in Probability","date_published":"2017-11-21T00:00:00Z","article_number":"63","ec_funded":1,"publist_id":"7265","file_date_updated":"2020-07-14T12:47:00Z","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","publication_status":"published","year":"2017","volume":22,"date_created":"2018-12-11T11:47:07Z","date_updated":"2023-09-07T12:38:08Z","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"149"}]},"author":[{"full_name":"Alt, Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","last_name":"Alt","first_name":"Johannes"}],"publication_identifier":{"issn":["1083589X"]},"month":"11","project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1214/17-ECP97"},{"publication":"Electronic Communications in Probability","citation":{"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.","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).","ista":"Erdös L, Schröder DJ. 2017. Fluctuations of functions of Wigner matrices. Electronic Communications in Probability. 21, 86.","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","ieee":"L. Erdös and D. J. Schröder, “Fluctuations of functions of Wigner matrices,” Electronic Communications in Probability, vol. 21. Institute of Mathematical Statistics, 2017.","ama":"Erdös L, Schröder DJ. Fluctuations of functions of Wigner matrices. Electronic Communications in Probability. 2017;21. doi:10.1214/16-ECP38"},"date_published":"2017-01-02T00:00:00Z","scopus_import":1,"day":"02","has_accepted_license":"1","_id":"1144","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Fluctuations of functions of Wigner matrices","status":"public","ddc":["510"],"intvolume":" 21","pubrep_id":"747","oa_version":"Published Version","file":[{"creator":"system","content_type":"application/pdf","file_size":440770,"access_level":"open_access","file_name":"IST-2017-747-v1+1_euclid.ecp.1483347665.pdf","date_updated":"2018-12-12T10:18:10Z","date_created":"2018-12-12T10:18:10Z","file_id":"5329","relation":"main_file"}],"type":"journal_article","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]."}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"doi":"10.1214/16-ECP38","language":[{"iso":"eng"}],"month":"01","year":"2017","acknowledgement":"Partially supported by the IST Austria Excellence Scholarship.","publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","author":[{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","first_name":"Dominik J","last_name":"Schröder","full_name":"Schröder, Dominik J"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"6179"}]},"date_updated":"2023-09-07T12:54:12Z","date_created":"2018-12-11T11:50:23Z","volume":21,"article_number":"86","file_date_updated":"2018-12-12T10:18:10Z","publist_id":"6214","ec_funded":1},{"issue":"3-4","abstract":[{"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.","lang":"eng"}],"type":"journal_article","file":[{"date_updated":"2020-07-14T12:45:00Z","date_created":"2018-12-12T10:08:05Z","checksum":"67afa85ff1e220cbc1f9f477a828513c","file_id":"4665","relation":"main_file","creator":"system","content_type":"application/pdf","file_size":1615755,"file_name":"IST-2016-489-v1+1_s00440-015-0692-y.pdf","access_level":"open_access"}],"oa_version":"Published Version","pubrep_id":"489","intvolume":" 167","ddc":["530"],"status":"public","title":"Delocalization for a class of random block band matrices","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"1528","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","scopus_import":"1","date_published":"2017-04-01T00:00:00Z","page":"673 - 776","article_type":"original","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","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.","short":"Z. Bao, L. Erdös, Probability Theory and Related Fields 167 (2017) 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.","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."},"publication":"Probability Theory and Related Fields","publist_id":"5644","ec_funded":1,"file_date_updated":"2020-07-14T12:45:00Z","volume":167,"date_updated":"2023-09-20T09:42:12Z","date_created":"2018-12-11T11:52:32Z","author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3036-1475","first_name":"Zhigang","last_name":"Bao","full_name":"Bao, Zhigang"},{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"}],"department":[{"_id":"LaEr"}],"publisher":"Springer","publication_status":"published","year":"2017","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.","publication_identifier":{"issn":["01788051"]},"month":"04","language":[{"iso":"eng"}],"doi":"10.1007/s00440-015-0692-y","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"isi":1,"quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000398842700004"]}},{"day":"01","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","scopus_import":"1","date_published":"2017-12-01T00:00:00Z","page":"667 - 727","publication":"Probability Theory and Related Fields","citation":{"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.","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.","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","ista":"Ajanki OH, Erdös L, Krüger TH. 2017. Universality for general Wigner-type matrices. Probability Theory and Related Fields. 169(3–4), 667–727.","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","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."},"abstract":[{"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.","lang":"eng"}],"issue":"3-4","type":"journal_article","file":[{"access_level":"open_access","file_name":"IST-2017-657-v1+2_s00440-016-0740-2.pdf","file_size":988843,"content_type":"application/pdf","creator":"system","relation":"main_file","file_id":"4686","checksum":"29f5a72c3f91e408aeb9e78344973803","date_created":"2018-12-12T10:08:25Z","date_updated":"2020-07-14T12:44:44Z"}],"oa_version":"Published Version","pubrep_id":"657","title":"Universality for general Wigner-type matrices","ddc":["510","530"],"status":"public","intvolume":" 169","_id":"1337","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","month":"12","publication_identifier":{"issn":["01788051"]},"language":[{"iso":"eng"}],"doi":"10.1007/s00440-016-0740-2","isi":1,"quality_controlled":"1","project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000414358400002"]},"oa":1,"file_date_updated":"2020-07-14T12:44:44Z","publist_id":"5930","ec_funded":1,"date_updated":"2023-09-20T11:14:17Z","date_created":"2018-12-11T11:51:27Z","volume":169,"author":[{"full_name":"Ajanki, Oskari H","id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87","first_name":"Oskari H","last_name":"Ajanki"},{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","last_name":"Krüger","first_name":"Torben H"}],"publication_status":"published","publisher":"Springer","department":[{"_id":"LaEr"}],"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). ","year":"2017"},{"pubrep_id":"722","file":[{"access_level":"open_access","file_name":"IST-2016-722-v1+1_s00220-016-2805-6.pdf","creator":"system","content_type":"application/pdf","file_size":1033743,"file_id":"5102","relation":"main_file","checksum":"ddff79154c3daf27237de5383b1264a9","date_updated":"2020-07-14T12:44:39Z","date_created":"2018-12-12T10:14:47Z"}],"oa_version":"Published Version","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"1207","ddc":["530"],"title":"Local law of addition of random matrices on optimal scale","status":"public","intvolume":" 349","abstract":[{"lang":"eng","text":"The eigenvalue distribution of the sum of two large Hermitian matrices, when one of them is conjugated by a Haar distributed unitary matrix, is asymptotically given by the free convolution of their spectral distributions. We prove that this convergence also holds locally in the bulk of the spectrum, down to the optimal scales larger than the eigenvalue spacing. The corresponding eigenvectors are fully delocalized. Similar results hold for the sum of two real symmetric matrices, when one is conjugated by Haar orthogonal matrix."}],"issue":"3","type":"journal_article","date_published":"2017-02-01T00:00:00Z","publication":"Communications in Mathematical Physics","citation":{"chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Law of Addition of Random Matrices on Optimal Scale.” Communications in Mathematical Physics. Springer, 2017. https://doi.org/10.1007/s00220-016-2805-6.","mla":"Bao, Zhigang, et al. “Local Law of Addition of Random Matrices on Optimal Scale.” Communications in Mathematical Physics, vol. 349, no. 3, Springer, 2017, pp. 947–90, doi:10.1007/s00220-016-2805-6.","short":"Z. Bao, L. Erdös, K. Schnelli, Communications in Mathematical Physics 349 (2017) 947–990.","ista":"Bao Z, Erdös L, Schnelli K. 2017. Local law of addition of random matrices on optimal scale. Communications in Mathematical Physics. 349(3), 947–990.","apa":"Bao, Z., Erdös, L., & Schnelli, K. (2017). Local law of addition of random matrices on optimal scale. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-016-2805-6","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Local law of addition of random matrices on optimal scale,” Communications in Mathematical Physics, vol. 349, no. 3. Springer, pp. 947–990, 2017.","ama":"Bao Z, Erdös L, Schnelli K. Local law of addition of random matrices on optimal scale. Communications in Mathematical Physics. 2017;349(3):947-990. doi:10.1007/s00220-016-2805-6"},"page":"947 - 990","day":"01","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","scopus_import":"1","author":[{"full_name":"Bao, Zhigang","orcid":"0000-0003-3036-1475","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","last_name":"Bao","first_name":"Zhigang"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"full_name":"Schnelli, Kevin","last_name":"Schnelli","first_name":"Kevin","orcid":"0000-0003-0954-3231","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2018-12-11T11:50:43Z","date_updated":"2023-09-20T11:16:57Z","volume":349,"year":"2017","publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Springer","file_date_updated":"2020-07-14T12:44:39Z","publist_id":"6141","ec_funded":1,"doi":"10.1007/s00220-016-2805-6","language":[{"iso":"eng"}],"external_id":{"isi":["000393696700005"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","isi":1,"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"month":"02","publication_identifier":{"issn":["00103616"]}},{"article_number":"22","file_date_updated":"2018-12-12T10:15:29Z","publist_id":"6370","publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","year":"2017","date_created":"2018-12-11T11:49:44Z","date_updated":"2023-09-22T09:27:51Z","volume":22,"author":[{"last_name":"Nemish","first_name":"Yuriy","orcid":"0000-0002-7327-856X","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","full_name":"Nemish, Yuriy"}],"month":"02","publication_identifier":{"issn":["10836489"]},"isi":1,"quality_controlled":"1","external_id":{"isi":["000396611900022"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"language":[{"iso":"eng"}],"doi":"10.1214/17-EJP38","type":"journal_article","abstract":[{"text":"We consider products of independent square non-Hermitian random matrices. More precisely, let X1,…, Xn be independent N × N random matrices with independent entries (real or complex with independent real and imaginary parts) with zero mean and variance 1/N. Soshnikov-O’Rourke [19] and Götze-Tikhomirov [15] showed that the empirical spectral distribution of the product of n random matrices with iid entries converges to (equation found). We prove that if the entries of the matrices X1,…, Xn are independent (but not necessarily identically distributed) and satisfy uniform subexponential decay condition, then in the bulk the convergence of the ESD of X1,…, Xn to (0.1) holds up to the scale N–1/2+ε.","lang":"eng"}],"status":"public","title":"Local law for the product of independent non-Hermitian random matrices with independent entries","ddc":["510"],"intvolume":" 22","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"1023","file":[{"file_name":"IST-2017-802-v1+1_euclid.ejp.1487991681.pdf","access_level":"open_access","file_size":742275,"content_type":"application/pdf","creator":"system","relation":"main_file","file_id":"5149","date_updated":"2018-12-12T10:15:29Z","date_created":"2018-12-12T10:15:29Z"}],"oa_version":"Published Version","pubrep_id":"802","scopus_import":"1","day":"06","has_accepted_license":"1","article_processing_charge":"No","publication":"Electronic Journal of Probability","citation":{"ama":"Nemish Y. Local law for the product of independent non-Hermitian random matrices with independent entries. Electronic Journal of Probability. 2017;22. doi:10.1214/17-EJP38","ista":"Nemish Y. 2017. Local law for the product of independent non-Hermitian random matrices with independent entries. Electronic Journal of Probability. 22, 22.","apa":"Nemish, Y. (2017). Local law for the product of independent non-Hermitian random matrices with independent entries. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/17-EJP38","ieee":"Y. Nemish, “Local law for the product of independent non-Hermitian random matrices with independent entries,” Electronic Journal of Probability, vol. 22. Institute of Mathematical Statistics, 2017.","mla":"Nemish, Yuriy. “Local Law for the Product of Independent Non-Hermitian Random Matrices with Independent Entries.” Electronic Journal of Probability, vol. 22, 22, Institute of Mathematical Statistics, 2017, doi:10.1214/17-EJP38.","short":"Y. Nemish, Electronic Journal of Probability 22 (2017).","chicago":"Nemish, Yuriy. “Local Law for the Product of Independent Non-Hermitian Random Matrices with Independent Entries.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/17-EJP38."},"date_published":"2017-02-06T00:00:00Z"},{"year":"2017","publication_status":"published","publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"author":[{"full_name":"Alt, Johannes","last_name":"Alt","first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","last_name":"Krüger","first_name":"Torben H","full_name":"Krüger, Torben H"}],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"149"}]},"date_created":"2018-12-11T11:49:40Z","date_updated":"2023-09-22T09:45:23Z","volume":22,"article_number":"25","file_date_updated":"2018-12-12T10:13:39Z","publist_id":"6386","ec_funded":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000396611900025"],"arxiv":["1606.07353"]},"oa":1,"isi":1,"quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"doi":"10.1214/17-EJP42","language":[{"iso":"eng"}],"month":"03","publication_identifier":{"issn":["10836489"]},"_id":"1010","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","title":"Local law for random Gram matrices","ddc":["510","539"],"intvolume":" 22","pubrep_id":"807","oa_version":"Published Version","file":[{"file_id":"5024","relation":"main_file","date_created":"2018-12-12T10:13:39Z","date_updated":"2018-12-12T10:13:39Z","access_level":"open_access","file_name":"IST-2017-807-v1+1_euclid.ejp.1488942016.pdf","creator":"system","file_size":639384,"content_type":"application/pdf"}],"type":"journal_article","abstract":[{"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∗. ","lang":"eng"}],"publication":"Electronic Journal of Probability","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","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.","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","ista":"Alt J, Erdös L, Krüger TH. 2017. Local law for random Gram matrices. Electronic Journal of Probability. 22, 25.","short":"J. Alt, L. Erdös, T.H. Krüger, Electronic Journal of Probability 22 (2017).","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.","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."},"date_published":"2017-03-08T00:00:00Z","scopus_import":"1","day":"08","has_accepted_license":"1","article_processing_charge":"No"},{"month":"10","language":[{"iso":"eng"}],"doi":"10.1016/j.aim.2017.08.028","quality_controlled":"1","isi":1,"project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"external_id":{"isi":["000412150400010"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1606.03076","open_access":"1"}],"ec_funded":1,"publist_id":"6935","date_updated":"2023-09-28T11:30:42Z","date_created":"2018-12-11T11:48:13Z","volume":319,"author":[{"full_name":"Bao, Zhigang","last_name":"Bao","first_name":"Zhigang","orcid":"0000-0003-3036-1475","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","full_name":"Erdös, László"},{"orcid":"0000-0003-0954-3231","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","last_name":"Schnelli","first_name":"Kevin","full_name":"Schnelli, Kevin"}],"publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Academic Press","year":"2017","acknowledgement":"Partially supported by ERC Advanced Grant RANMAT No. 338804, Hong Kong RGC grant ECS 26301517, and the Göran Gustafsson Foundation","day":"15","article_processing_charge":"No","scopus_import":"1","date_published":"2017-10-15T00:00:00Z","page":"251 - 291","publication":"Advances in Mathematics","citation":{"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.","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.","ista":"Bao Z, Erdös L, Schnelli K. 2017. Convergence rate for spectral distribution of addition of random matrices. Advances in Mathematics. 319, 251–291.","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","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.","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"},"abstract":[{"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.","lang":"eng"}],"type":"journal_article","oa_version":"Submitted Version","status":"public","title":"Convergence rate for spectral distribution of addition of random matrices","intvolume":" 319","_id":"733","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1"},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"447","status":"public","title":"Fluctuations of the competition interface in presence of shocks","intvolume":" 9","oa_version":"Submitted Version","type":"journal_article","abstract":[{"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).","lang":"eng"}],"publication":"Revista Latino-Americana de Probabilidade e Estatística","citation":{"short":"P. Ferrari, P. Nejjar, Revista Latino-Americana de Probabilidade e Estatística 9 (2017) 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.","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.","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","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."},"article_type":"original","page":"299 - 325","date_published":"2017-03-23T00:00:00Z","scopus_import":"1","day":"23","article_processing_charge":"No","year":"2017","publication_status":"published","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"publisher":"Instituto Nacional de Matematica Pura e Aplicada","author":[{"full_name":"Ferrari, Patrik","last_name":"Ferrari","first_name":"Patrik"},{"id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","last_name":"Nejjar","first_name":"Peter","full_name":"Nejjar, Peter"}],"date_updated":"2023-10-10T13:10:32Z","date_created":"2018-12-11T11:46:31Z","volume":9,"ec_funded":1,"publist_id":"7376","oa":1,"main_file_link":[{"open_access":"1","url":"http://alea.impa.br/articles/v14/14-17.pdf"}],"quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"doi":"10.30757/ALEA.v14-17","language":[{"iso":"eng"}],"month":"03"},{"month":"12","project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"quality_controlled":"1","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1409.4979"}],"language":[{"iso":"eng"}],"doi":"10.1214/16-AAP1193","publist_id":"6201","ec_funded":1,"publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"publication_status":"published","year":"2016","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.","volume":26,"date_updated":"2021-01-12T06:48:43Z","date_created":"2018-12-11T11:50:27Z","author":[{"full_name":"Lee, Ji","last_name":"Lee","first_name":"Ji"},{"last_name":"Schnelli","first_name":"Kevin","orcid":"0000-0003-0954-3231","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","full_name":"Schnelli, Kevin"}],"scopus_import":1,"day":"15","page":"3786 - 3839","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","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.","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","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.","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.","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."},"publication":"Annals of Applied Probability","date_published":"2016-12-15T00:00:00Z","type":"journal_article","issue":"6","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."}],"intvolume":" 26","status":"public","title":"Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1157","oa_version":"Preprint"},{"month":"01","doi":"10.1214/15-AOP1023","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1405.6634"}],"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"quality_controlled":"1","publist_id":"6115","ec_funded":1,"author":[{"full_name":"Lee, Jioon","first_name":"Jioon","last_name":"Lee"},{"full_name":"Schnelli, Kevin","last_name":"Schnelli","first_name":"Kevin","orcid":"0000-0003-0954-3231","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Ben","last_name":"Stetler","full_name":"Stetler, Ben"},{"full_name":"Yau, Horngtzer","first_name":"Horngtzer","last_name":"Yau"}],"volume":44,"date_created":"2018-12-11T11:50:47Z","date_updated":"2021-01-12T06:49:10Z","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. ","year":"2016","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","publication_status":"published","day":"01","scopus_import":1,"date_published":"2016-01-01T00:00:00Z","citation":{"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.","short":"J. Lee, K. Schnelli, B. Stetler, H. Yau, Annals of Probability 44 (2016) 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.","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.","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","ista":"Lee J, Schnelli K, Stetler B, Yau H. 2016. Bulk universality for deformed wigner matrices. Annals of Probability. 44(3), 2349–2425.","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"},"publication":"Annals of Probability","page":"2349 - 2425","issue":"3","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."}],"type":"journal_article","oa_version":"Preprint","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1219","intvolume":" 44","status":"public","title":"Bulk universality for deformed wigner matrices"},{"type":"journal_article","issue":"3","publist_id":"6112","abstract":[{"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.","lang":"eng"}],"_id":"1223","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","year":"2016","intvolume":" 6","publisher":"European Mathematical Society","department":[{"_id":"LaEr"}],"publication_status":"published","title":"Localization for transversally periodic random potentials on binary trees","status":"public","author":[{"last_name":"Froese","first_name":"Richard","full_name":"Froese, Richard"},{"full_name":"Lee, Darrick","last_name":"Lee","first_name":"Darrick"},{"first_name":"Christian","last_name":"Sadel","id":"4760E9F8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8255-3968","full_name":"Sadel, Christian"},{"first_name":"Wolfgang","last_name":"Spitzer","full_name":"Spitzer, Wolfgang"},{"last_name":"Stolz","first_name":"Günter","full_name":"Stolz, Günter"}],"volume":6,"oa_version":"Preprint","date_updated":"2021-01-12T06:49:12Z","date_created":"2018-12-11T11:50:48Z","scopus_import":1,"day":"01","month":"01","main_file_link":[{"url":"https://arxiv.org/abs/1408.3961","open_access":"1"}],"oa":1,"citation":{"short":"R. Froese, D. Lee, C. Sadel, W. Spitzer, G. Stolz, Journal of Spectral Theory 6 (2016) 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.","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.","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","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.","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","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."},"publication":"Journal of Spectral Theory","page":"557 - 600","quality_controlled":"1","doi":"10.4171/JST/132","date_published":"2016-01-01T00:00:00Z","language":[{"iso":"eng"}]},{"date_updated":"2021-01-12T06:49:26Z","date_created":"2018-12-11T11:50:59Z","volume":343,"author":[{"id":"4760E9F8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8255-3968","first_name":"Christian","last_name":"Sadel","full_name":"Sadel, Christian"},{"first_name":"Bálint","last_name":"Virág","full_name":"Virág, Bálint"}],"publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Springer","year":"2016","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.","file_date_updated":"2020-07-14T12:44:42Z","publist_id":"6067","ec_funded":1,"language":[{"iso":"eng"}],"doi":"10.1007/s00220-016-2600-4","quality_controlled":"1","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"month":"05","file":[{"access_level":"open_access","file_name":"IST-2016-703-v1+1_s00220-016-2600-4.pdf","file_size":800792,"content_type":"application/pdf","creator":"system","relation":"main_file","file_id":"5119","checksum":"4fb2411d9c2f56676123165aad46c828","date_updated":"2020-07-14T12:44:42Z","date_created":"2018-12-12T10:15:02Z"}],"oa_version":"Published Version","pubrep_id":"703","status":"public","ddc":["510","539"],"title":"A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes","intvolume":" 343","_id":"1257","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","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."}],"issue":"3","type":"journal_article","date_published":"2016-05-01T00:00:00Z","page":"881 - 919","publication":"Communications in Mathematical Physics","citation":{"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.","short":"C. Sadel, B. Virág, Communications in Mathematical Physics 343 (2016) 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.","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.","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","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.","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"},"day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","scopus_import":1},{"project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1407.5606"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1002/cpa.21624","month":"10","publisher":"Wiley-Blackwell","department":[{"_id":"LaEr"}],"publication_status":"published","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.","year":"2016","volume":69,"date_updated":"2021-01-12T06:49:35Z","date_created":"2018-12-11T11:51:07Z","author":[{"last_name":"Bourgade","first_name":"Paul","full_name":"Bourgade, Paul"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"Erdös, László"},{"full_name":"Yau, Horngtzer","first_name":"Horngtzer","last_name":"Yau"},{"first_name":"Jun","last_name":"Yin","full_name":"Yin, Jun"}],"publist_id":"6036","ec_funded":1,"page":"1815 - 1881","citation":{"short":"P. Bourgade, L. Erdös, H. Yau, J. Yin, Communications on Pure and Applied Mathematics 69 (2016) 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.","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.","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","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."},"publication":"Communications on Pure and Applied Mathematics","date_published":"2016-10-01T00:00:00Z","scopus_import":1,"day":"01","intvolume":" 69","status":"public","title":"Fixed energy universality for generalized wigner matrices","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1280","oa_version":"Preprint","type":"journal_article","issue":"10","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."}]},{"doi":"10.1016/j.jfa.2016.04.006","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1508.05905"}],"project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"quality_controlled":"1","month":"08","author":[{"full_name":"Bao, Zhigang","last_name":"Bao","first_name":"Zhigang","orcid":"0000-0003-3036-1475","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"},{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0954-3231","first_name":"Kevin","last_name":"Schnelli","full_name":"Schnelli, Kevin"}],"volume":271,"date_created":"2018-12-11T11:52:00Z","date_updated":"2021-01-12T06:50:42Z","year":"2016","department":[{"_id":"LaEr"}],"publisher":"Academic Press","publication_status":"published","publist_id":"5764","ec_funded":1,"date_published":"2016-08-01T00:00:00Z","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","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.","short":"Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 271 (2016) 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.","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."},"publication":"Journal of Functional Analysis","page":"672 - 719","day":"01","scopus_import":1,"oa_version":"Preprint","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1434","intvolume":" 271","title":"Local stability of the free additive convolution","status":"public","issue":"3","abstract":[{"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.","lang":"eng"}],"type":"journal_article"},{"type":"journal_article","issue":"2","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. "}],"intvolume":" 163","status":"public","ddc":["510"],"title":"Local spectral statistics of Gaussian matrices with correlated entries","_id":"1489","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","file":[{"creator":"system","content_type":"application/pdf","file_size":660602,"access_level":"open_access","file_name":"IST-2016-516-v1+1_s10955-016-1479-y.pdf","checksum":"7139598dcb1cafbe6866bd2bfd732b33","date_updated":"2020-07-14T12:44:57Z","date_created":"2018-12-12T10:11:16Z","file_id":"4869","relation":"main_file"}],"pubrep_id":"516","scopus_import":1,"article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"01","page":"280 - 302","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","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.","short":"O.H. Ajanki, L. Erdös, T.H. Krüger, Journal of Statistical Physics 163 (2016) 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.","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."},"publication":"Journal of Statistical Physics","date_published":"2016-04-01T00:00:00Z","ec_funded":1,"publist_id":"5698","file_date_updated":"2020-07-14T12:44:57Z","department":[{"_id":"LaEr"}],"publisher":"Springer","publication_status":"published","year":"2016","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.","volume":163,"date_updated":"2021-01-12T06:51:05Z","date_created":"2018-12-11T11:52:19Z","author":[{"id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87","first_name":"Oskari H","last_name":"Ajanki","full_name":"Ajanki, Oskari H"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","full_name":"Erdös, László"},{"full_name":"Krüger, Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","first_name":"Torben H","last_name":"Krüger"}],"month":"04","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"language":[{"iso":"eng"}],"doi":"10.1007/s10955-016-1479-y"},{"issue":"7","abstract":[{"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 rΔdr+λ on ℤd, where r is an orthogonal radial projection, Δd the discrete adjacency operator (Laplacian) on ℤd and λ a random potential. ","lang":"eng"}],"type":"journal_article","oa_version":"Preprint","_id":"1608","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","intvolume":" 17","title":"Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel","status":"public","day":"01","scopus_import":1,"date_published":"2016-07-01T00:00:00Z","citation":{"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","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.","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","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.","short":"C. Sadel, Annales Henri Poincare 17 (2016) 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."},"publication":"Annales Henri Poincare","page":"1631 - 1675","ec_funded":1,"publist_id":"5558","author":[{"id":"4760E9F8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8255-3968","first_name":"Christian","last_name":"Sadel","full_name":"Sadel, Christian"}],"volume":17,"date_updated":"2021-01-12T06:51:58Z","date_created":"2018-12-11T11:53:00Z","year":"2016","publisher":"Birkhäuser","department":[{"_id":"LaEr"}],"publication_status":"published","month":"07","doi":"10.1007/s00023-015-0456-3","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1501.04287"}],"oa":1,"project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734"}],"quality_controlled":"1"},{"date_published":"2016-02-01T00:00:00Z","citation":{"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","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.","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","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.","short":"J. Lee, K. Schnelli, Probability Theory and Related Fields 164 (2016) 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."},"publication":"Probability Theory and Related Fields","page":"165 - 241","day":"01","scopus_import":1,"oa_version":"Preprint","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"1881","intvolume":" 164","status":"public","title":"Extremal eigenvalues and eigenvectors of deformed Wigner matrices","issue":"1-2","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. "}],"type":"journal_article","doi":"10.1007/s00440-014-0610-8","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1310.7057"}],"project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","month":"02","author":[{"last_name":"Lee","first_name":"Jioon","full_name":"Lee, Jioon"},{"first_name":"Kevin","last_name":"Schnelli","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin"}],"volume":164,"date_created":"2018-12-11T11:54:31Z","date_updated":"2021-01-12T06:53:49Z","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.","year":"2016","department":[{"_id":"LaEr"}],"publisher":"Springer","publication_status":"published","ec_funded":1,"publist_id":"5215"},{"issue":"1","publist_id":"5672","abstract":[{"text":"This paper is aimed at deriving the universality of the largest eigenvalue of a class of high-dimensional real or complex sample covariance matrices of the form W N =Σ 1/2XX∗Σ 1/2 . Here, X = (xij )M,N is an M× N random matrix with independent entries xij , 1 ≤ i M,≤ 1 ≤ j ≤ N such that Exij = 0, E|xij |2 = 1/N . On dimensionality, we assume that M = M(N) and N/M → d ε (0, ∞) as N ∞→. For a class of general deterministic positive-definite M × M matrices Σ , under some additional assumptions on the distribution of xij 's, we show that the limiting behavior of the largest eigenvalue of W N is universal, via pursuing a Green function comparison strategy raised in [Probab. Theory Related Fields 154 (2012) 341-407, Adv. Math. 229 (2012) 1435-1515] by Erd″os, Yau and Yin for Wigner matrices and extended by Pillai and Yin [Ann. Appl. Probab. 24 (2014) 935-1001] to sample covariance matrices in the null case (&Epsi = I ). Consequently, in the standard complex case (Ex2 ij = 0), combing this universality property and the results known for Gaussian matrices obtained by El Karoui in [Ann. Probab. 35 (2007) 663-714] (nonsingular case) and Onatski in [Ann. Appl. Probab. 18 (2008) 470-490] (singular case), we show that after an appropriate normalization the largest eigenvalue of W N converges weakly to the type 2 Tracy-Widom distribution TW2 . Moreover, in the real case, we show that whenΣ is spiked with a fixed number of subcritical spikes, the type 1 Tracy-Widom limit TW1 holds for the normalized largest eigenvalue of W N , which extends a result of Féral and Péché in [J. Math. Phys. 50 (2009) 073302] to the scenario of nondiagonal Σ and more generally distributed X . In summary, we establish the Tracy-Widom type universality for the largest eigenvalue of generally distributed sample covariance matrices under quite light assumptions on &Sigma . Applications of these limiting results to statistical signal detection and structure recognition of separable covariance matrices are also discussed.","lang":"eng"}],"type":"journal_article","volume":43,"oa_version":"Preprint","date_created":"2018-12-11T11:52:25Z","date_updated":"2021-01-12T06:51:14Z","author":[{"full_name":"Bao, Zhigang","last_name":"Bao","first_name":"Zhigang","orcid":"0000-0003-3036-1475","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Pan","first_name":"Guangming","full_name":"Pan, Guangming"},{"full_name":"Zhou, Wang","first_name":"Wang","last_name":"Zhou"}],"department":[{"_id":"LaEr"}],"intvolume":" 43","publisher":"Institute of Mathematical Statistics","publication_status":"published","status":"public","title":"Universality for the largest eigenvalue of sample covariance matrices with general population","acknowledgement":"B.Z. was supported in part by NSFC Grant 11071213, ZJNSF Grant R6090034 and SRFDP Grant 20100101110001. P.G. was supported in part by the Ministry of Education, Singapore, under Grant ARC 14/11. Z.W. was supported in part by the Ministry of Education, Singapore, under Grant ARC 14/11, and by a Grant R-155-000-131-112 at the National University of Singapore\r\n","_id":"1505","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2015","month":"02","day":"01","language":[{"iso":"eng"}],"doi":"10.1214/14-AOS1281","date_published":"2015-02-01T00:00:00Z","page":"382 - 421","quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/1304.5690","open_access":"1"}],"citation":{"apa":"Bao, Z., Pan, G., & Zhou, W. (2015). Universality for the largest eigenvalue of sample covariance matrices with general population. Annals of Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/14-AOS1281","ieee":"Z. Bao, G. Pan, and W. Zhou, “Universality for the largest eigenvalue of sample covariance matrices with general population,” Annals of Statistics, vol. 43, no. 1. Institute of Mathematical Statistics, pp. 382–421, 2015.","ista":"Bao Z, Pan G, Zhou W. 2015. Universality for the largest eigenvalue of sample covariance matrices with general population. Annals of Statistics. 43(1), 382–421.","ama":"Bao Z, Pan G, Zhou W. Universality for the largest eigenvalue of sample covariance matrices with general population. Annals of Statistics. 2015;43(1):382-421. doi:10.1214/14-AOS1281","chicago":"Bao, Zhigang, Guangming Pan, and Wang Zhou. “Universality for the Largest Eigenvalue of Sample Covariance Matrices with General Population.” Annals of Statistics. Institute of Mathematical Statistics, 2015. https://doi.org/10.1214/14-AOS1281.","short":"Z. Bao, G. Pan, W. Zhou, Annals of Statistics 43 (2015) 382–421.","mla":"Bao, Zhigang, et al. “Universality for the Largest Eigenvalue of Sample Covariance Matrices with General Population.” Annals of Statistics, vol. 43, no. 1, Institute of Mathematical Statistics, 2015, pp. 382–421, doi:10.1214/14-AOS1281."},"oa":1,"publication":"Annals of Statistics"},{"type":"journal_article","issue":"8","publist_id":"5669","abstract":[{"lang":"eng","text":"We consider generalized Wigner ensembles and general β-ensembles with analytic potentials for any β ≥ 1. The recent universality results in particular assert that the local averages of consecutive eigenvalue gaps in the bulk of the spectrum are universal in the sense that they coincide with those of the corresponding Gaussian β-ensembles. In this article, we show that local averaging is not necessary for this result, i.e. we prove that the single gap distributions in the bulk are universal. In fact, with an additional step, our result can be extended to any C4(ℝ) potential."}],"year":"2015","_id":"1508","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 17","department":[{"_id":"LaEr"}],"publisher":"European Mathematical Society","publication_status":"published","status":"public","title":"Gap universality of generalized Wigner and β ensembles","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"Erdös, László"},{"first_name":"Horng","last_name":"Yau","full_name":"Yau, Horng"}],"volume":17,"oa_version":"Preprint","date_updated":"2021-01-12T06:51:15Z","date_created":"2018-12-11T11:52:26Z","scopus_import":1,"day":"01","month":"08","main_file_link":[{"url":"http://arxiv.org/abs/1211.3786","open_access":"1"}],"citation":{"ista":"Erdös L, Yau H. 2015. Gap universality of generalized Wigner and β ensembles. Journal of the European Mathematical Society. 17(8), 1927–2036.","ieee":"L. Erdös and H. Yau, “Gap universality of generalized Wigner and β ensembles,” Journal of the European Mathematical Society, vol. 17, no. 8. European Mathematical Society, pp. 1927–2036, 2015.","apa":"Erdös, L., & Yau, H. (2015). Gap universality of generalized Wigner and β ensembles. Journal of the European Mathematical Society. European Mathematical Society. https://doi.org/10.4171/JEMS/548","ama":"Erdös L, Yau H. Gap universality of generalized Wigner and β ensembles. Journal of the European Mathematical Society. 2015;17(8):1927-2036. doi:10.4171/JEMS/548","chicago":"Erdös, László, and Horng Yau. “Gap Universality of Generalized Wigner and β Ensembles.” Journal of the European Mathematical Society. European Mathematical Society, 2015. https://doi.org/10.4171/JEMS/548.","mla":"Erdös, László, and Horng Yau. “Gap Universality of Generalized Wigner and β Ensembles.” Journal of the European Mathematical Society, vol. 17, no. 8, European Mathematical Society, 2015, pp. 1927–2036, doi:10.4171/JEMS/548.","short":"L. Erdös, H. Yau, Journal of the European Mathematical Society 17 (2015) 1927–2036."},"oa":1,"publication":"Journal of the European Mathematical Society","page":"1927 - 2036","quality_controlled":"1","doi":"10.4171/JEMS/548","date_published":"2015-08-01T00:00:00Z","language":[{"iso":"eng"}]},{"oa_version":"Preprint","volume":21,"date_updated":"2021-01-12T06:51:14Z","date_created":"2018-12-11T11:52:25Z","author":[{"full_name":"Bao, Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3036-1475","first_name":"Zhigang","last_name":"Bao"},{"last_name":"Pan","first_name":"Guangming","full_name":"Pan, Guangming"},{"first_name":"Wang","last_name":"Zhou","full_name":"Zhou, Wang"}],"publisher":"Bernoulli Society for Mathematical Statistics and Probability","department":[{"_id":"LaEr"}],"intvolume":" 21","title":"The logarithmic law of random determinant","status":"public","publication_status":"published","_id":"1506","year":"2015","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"3","publist_id":"5671","abstract":[{"text":"Consider the square random matrix An = (aij)n,n, where {aij:= a(n)ij , i, j = 1, . . . , n} is a collection of independent real random variables with means zero and variances one. Under the additional moment condition supn max1≤i,j ≤n Ea4ij <∞, we prove Girko's logarithmic law of det An in the sense that as n→∞ log | detAn| ? (1/2) log(n-1)! d/→√(1/2) log n N(0, 1).","lang":"eng"}],"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.3150/14-BEJ615","date_published":"2015-08-01T00:00:00Z","page":"1600 - 1628","quality_controlled":"1","citation":{"chicago":"Bao, Zhigang, Guangming Pan, and Wang Zhou. “The Logarithmic Law of Random Determinant.” Bernoulli. Bernoulli Society for Mathematical Statistics and Probability, 2015. https://doi.org/10.3150/14-BEJ615.","mla":"Bao, Zhigang, et al. “The Logarithmic Law of Random Determinant.” Bernoulli, vol. 21, no. 3, Bernoulli Society for Mathematical Statistics and Probability, 2015, pp. 1600–28, doi:10.3150/14-BEJ615.","short":"Z. Bao, G. Pan, W. Zhou, Bernoulli 21 (2015) 1600–1628.","ista":"Bao Z, Pan G, Zhou W. 2015. The logarithmic law of random determinant. Bernoulli. 21(3), 1600–1628.","apa":"Bao, Z., Pan, G., & Zhou, W. (2015). The logarithmic law of random determinant. Bernoulli. Bernoulli Society for Mathematical Statistics and Probability. https://doi.org/10.3150/14-BEJ615","ieee":"Z. Bao, G. Pan, and W. Zhou, “The logarithmic law of random determinant,” Bernoulli, vol. 21, no. 3. Bernoulli Society for Mathematical Statistics and Probability, pp. 1600–1628, 2015.","ama":"Bao Z, Pan G, Zhou W. The logarithmic law of random determinant. Bernoulli. 2015;21(3):1600-1628. doi:10.3150/14-BEJ615"},"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1208.5823"}],"oa":1,"publication":"Bernoulli","month":"08","day":"01"},{"page":"3413 - 3426","quality_controlled":"1","citation":{"ama":"Bao Z, Pan G, Zhou W. Asymptotic mutual information statistics of MIMO channels and CLT of sample covariance matrices. IEEE Transactions on Information Theory. 2015;61(6):3413-3426. doi:10.1109/TIT.2015.2421894","ista":"Bao Z, Pan G, Zhou W. 2015. Asymptotic mutual information statistics of MIMO channels and CLT of sample covariance matrices. IEEE Transactions on Information Theory. 61(6), 3413–3426.","ieee":"Z. Bao, G. Pan, and W. Zhou, “Asymptotic mutual information statistics of MIMO channels and CLT of sample covariance matrices,” IEEE Transactions on Information Theory, vol. 61, no. 6. IEEE, pp. 3413–3426, 2015.","apa":"Bao, Z., Pan, G., & Zhou, W. (2015). Asymptotic mutual information statistics of MIMO channels and CLT of sample covariance matrices. IEEE Transactions on Information Theory. IEEE. https://doi.org/10.1109/TIT.2015.2421894","mla":"Bao, Zhigang, et al. “Asymptotic Mutual Information Statistics of MIMO Channels and CLT of Sample Covariance Matrices.” IEEE Transactions on Information Theory, vol. 61, no. 6, IEEE, 2015, pp. 3413–26, doi:10.1109/TIT.2015.2421894.","short":"Z. Bao, G. Pan, W. Zhou, IEEE Transactions on Information Theory 61 (2015) 3413–3426.","chicago":"Bao, Zhigang, Guangming Pan, and Wang Zhou. “Asymptotic Mutual Information Statistics of MIMO Channels and CLT of Sample Covariance Matrices.” IEEE Transactions on Information Theory. IEEE, 2015. https://doi.org/10.1109/TIT.2015.2421894."},"publication":"IEEE Transactions on Information Theory","language":[{"iso":"eng"}],"date_published":"2015-06-01T00:00:00Z","doi":"10.1109/TIT.2015.2421894","scopus_import":1,"month":"06","day":"01","department":[{"_id":"LaEr"}],"intvolume":" 61","publisher":"IEEE","title":"Asymptotic mutual information statistics of MIMO channels and CLT of sample covariance matrices","publication_status":"published","status":"public","_id":"1585","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2015","acknowledgement":"G. Pan was supported by MOE Tier 2 under Grant 2014-T2-2-060 and in part by Tier 1 under Grant RG25/14 through the Nanyang Technological University, Singapore. W. Zhou was supported by the National University of Singapore, Singapore, under Grant R-155-000-131-112.\r\n","volume":61,"oa_version":"None","date_created":"2018-12-11T11:52:52Z","date_updated":"2021-01-12T06:51:46Z","author":[{"orcid":"0000-0003-3036-1475","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","last_name":"Bao","first_name":"Zhigang","full_name":"Bao, Zhigang"},{"first_name":"Guangming","last_name":"Pan","full_name":"Pan, Guangming"},{"first_name":"Wang","last_name":"Zhou","full_name":"Zhou, Wang"}],"type":"journal_article","publist_id":"5586","issue":"6","abstract":[{"lang":"eng","text":"In this paper, we consider the fluctuation of mutual information statistics of a multiple input multiple output channel communication systems without assuming that the entries of the channel matrix have zero pseudovariance. To this end, we also establish a central limit theorem of the linear spectral statistics for sample covariance matrices under general moment conditions by removing the restrictions imposed on the second moment and fourth moment on the matrix entries in Bai and Silverstein (2004)."}]},{"month":"09","day":"01","scopus_import":1,"doi":"10.1142/S0129055X1550018X","date_published":"2015-09-01T00:00:00Z","language":[{"iso":"eng"}],"publication":"Reviews in Mathematical Physics","citation":{"short":"J. Lee, K. Schnelli, Reviews in Mathematical Physics 27 (2015).","mla":"Lee, Jioon, and Kevin Schnelli. “Edge Universality for Deformed Wigner Matrices.” Reviews in Mathematical Physics, vol. 27, no. 8, 1550018, World Scientific Publishing, 2015, doi:10.1142/S0129055X1550018X.","chicago":"Lee, Jioon, and Kevin Schnelli. “Edge Universality for Deformed Wigner Matrices.” Reviews in Mathematical Physics. World Scientific Publishing, 2015. https://doi.org/10.1142/S0129055X1550018X.","ama":"Lee J, Schnelli K. Edge universality for deformed Wigner matrices. Reviews in Mathematical Physics. 2015;27(8). doi:10.1142/S0129055X1550018X","ieee":"J. Lee and K. Schnelli, “Edge universality for deformed Wigner matrices,” Reviews in Mathematical Physics, vol. 27, no. 8. World Scientific Publishing, 2015.","apa":"Lee, J., & Schnelli, K. (2015). Edge universality for deformed Wigner matrices. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/S0129055X1550018X","ista":"Lee J, Schnelli K. 2015. Edge universality for deformed Wigner matrices. Reviews in Mathematical Physics. 27(8), 1550018."},"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1407.8015"}],"oa":1,"quality_controlled":"1","abstract":[{"text":"We consider N × N random matrices of the form H = W + V where W is a real symmetric Wigner matrix and V 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 of W and V are typically of the same order. For a large class of diagonal matrices V, we show that the rescaled distribution of the extremal eigenvalues is given by the Tracy-Widom distribution F1 in the limit of large N. Our proofs also apply to the complex Hermitian setting, i.e. when W is a complex Hermitian Wigner matrix.","lang":"eng"}],"publist_id":"5475","issue":"8","article_number":"1550018","type":"journal_article","author":[{"full_name":"Lee, Jioon","first_name":"Jioon","last_name":"Lee"},{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0954-3231","first_name":"Kevin","last_name":"Schnelli","full_name":"Schnelli, Kevin"}],"date_updated":"2021-01-12T06:52:26Z","date_created":"2018-12-11T11:53:24Z","oa_version":"Preprint","volume":27,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1674","year":"2015","title":"Edge universality for deformed Wigner matrices","publication_status":"published","status":"public","publisher":"World Scientific Publishing","intvolume":" 27","department":[{"_id":"LaEr"}]},{"year":"2015","publication_status":"published","publisher":"Nature Publishing Group","department":[{"_id":"LaEr"}],"author":[{"first_name":"Johannes","last_name":"Knebel","full_name":"Knebel, Johannes"},{"last_name":"Weber","first_name":"Markus","full_name":"Weber, Markus"},{"last_name":"Krüger","first_name":"Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H"},{"full_name":"Frey, Erwin","first_name":"Erwin","last_name":"Frey"}],"date_updated":"2021-01-12T06:53:26Z","date_created":"2018-12-11T11:54:13Z","volume":6,"article_number":"6977","file_date_updated":"2020-07-14T12:45:17Z","publist_id":"5282","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"quality_controlled":"1","doi":"10.1038/ncomms7977","language":[{"iso":"eng"}],"month":"04","_id":"1824","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Evolutionary games of condensates in coupled birth-death processes","status":"public","ddc":["530"],"intvolume":" 6","pubrep_id":"451","file":[{"file_size":1151501,"content_type":"application/pdf","creator":"system","file_name":"IST-2016-451-v1+1_ncomms7977.pdf","access_level":"open_access","date_updated":"2020-07-14T12:45:17Z","date_created":"2018-12-12T10:16:54Z","checksum":"c4cffb5c8b245e658a34eac71a03e7cc","relation":"main_file","file_id":"5245"}],"oa_version":"Published Version","type":"journal_article","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."}],"publication":"Nature Communications","citation":{"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.","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).","ista":"Knebel J, Weber M, Krüger TH, Frey E. 2015. Evolutionary games of condensates in coupled birth-death processes. Nature Communications. 6, 6977.","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.","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","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"},"date_published":"2015-04-24T00:00:00Z","scopus_import":1,"day":"24","has_accepted_license":"1"},{"language":[{"iso":"eng"}],"doi":"10.1007/s00023-014-0333-5","project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"main_file_link":[{"url":"http://arxiv.org/abs/1309.5107","open_access":"1"}],"oa":1,"month":"03","date_created":"2018-12-11T11:54:26Z","date_updated":"2021-01-12T06:53:42Z","volume":16,"author":[{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"Knowles, Antti","last_name":"Knowles","first_name":"Antti"}],"publication_status":"published","publisher":"Springer","department":[{"_id":"LaEr"}],"year":"2015","ec_funded":1,"publist_id":"5233","date_published":"2015-03-01T00:00:00Z","page":"709 - 799","publication":"Annales Henri Poincare","citation":{"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.","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.","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.","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.","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","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"},"day":"01","scopus_import":1,"oa_version":"Preprint","status":"public","title":"The Altshuler–Shklovskii formulas for random band matrices II: The general case","intvolume":" 16","_id":"1864","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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"}],"issue":"3","type":"journal_article"},{"month":"02","day":"01","scopus_import":1,"language":[{"iso":"eng"}],"date_published":"2015-02-01T00:00:00Z","doi":"10.1007/s00220-014-2119-5","page":"1365 - 1416","quality_controlled":"1","citation":{"chicago":"Erdös, László, and Antti Knowles. “The Altshuler-Shklovskii Formulas for Random Band Matrices I: The Unimodular Case.” Communications in Mathematical Physics. Springer, 2015. https://doi.org/10.1007/s00220-014-2119-5.","mla":"Erdös, László, and Antti Knowles. “The Altshuler-Shklovskii Formulas for Random Band Matrices I: The Unimodular Case.” Communications in Mathematical Physics, vol. 333, no. 3, Springer, 2015, pp. 1365–416, doi:10.1007/s00220-014-2119-5.","short":"L. Erdös, A. Knowles, Communications in Mathematical Physics 333 (2015) 1365–1416.","ista":"Erdös L, Knowles A. 2015. The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case. Communications in Mathematical Physics. 333(3), 1365–1416.","apa":"Erdös, L., & Knowles, A. (2015). The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-014-2119-5","ieee":"L. Erdös and A. Knowles, “The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case,” Communications in Mathematical Physics, vol. 333, no. 3. Springer, pp. 1365–1416, 2015.","ama":"Erdös L, Knowles A. The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case. Communications in Mathematical Physics. 2015;333(3):1365-1416. doi:10.1007/s00220-014-2119-5"},"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1309.5106"}],"oa":1,"publication":"Communications in Mathematical Physics","issue":"3","publist_id":"4818","abstract":[{"text":"We consider the spectral statistics of large random band matrices on mesoscopic energy scales. We show that the correlation function of the local eigenvalue density exhibits a universal power law behaviour that differs from the Wigner-Dyson- Mehta statistics. This law had been predicted in the physics literature by Altshuler and Shklovskii in (Zh Eksp Teor Fiz (Sov Phys JETP) 91(64):220(127), 1986); it describes the correlations of the eigenvalue density in general metallic sampleswith weak disorder. Our result rigorously establishes the Altshuler-Shklovskii formulas for band matrices. In two dimensions, where the leading term vanishes owing to an algebraic cancellation, we identify the first non-vanishing term and show that it differs substantially from the prediction of Kravtsov and Lerner in (Phys Rev Lett 74:2563-2566, 1995). The proof is given in the current paper and its companion (Ann. H. Poincaré. arXiv:1309.5107, 2014). ","lang":"eng"}],"type":"journal_article","volume":333,"oa_version":"Preprint","date_updated":"2021-01-12T06:55:43Z","date_created":"2018-12-11T11:56:05Z","author":[{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"},{"last_name":"Knowles","first_name":"Antti","full_name":"Knowles, Antti"}],"publisher":"Springer","department":[{"_id":"LaEr"}],"intvolume":" 333","publication_status":"published","title":"The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case","status":"public","year":"2015","_id":"2166","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"day":"09","scopus_import":1,"date_published":"2015-10-09T00:00:00Z","citation":{"chicago":"Alt, Johannes. “The Local Semicircle Law for Random Matrices with a Fourfold Symmetry.” Journal of Mathematical Physics. American Institute of Physics, 2015. https://doi.org/10.1063/1.4932606.","short":"J. Alt, Journal of Mathematical Physics 56 (2015).","mla":"Alt, Johannes. “The Local Semicircle Law for Random Matrices with a Fourfold Symmetry.” Journal of Mathematical Physics, vol. 56, no. 10, 103301, American Institute of Physics, 2015, doi:10.1063/1.4932606.","apa":"Alt, J. (2015). The local semicircle law for random matrices with a fourfold symmetry. Journal of Mathematical Physics. American Institute of Physics. https://doi.org/10.1063/1.4932606","ieee":"J. Alt, “The local semicircle law for random matrices with a fourfold symmetry,” Journal of Mathematical Physics, vol. 56, no. 10. American Institute of Physics, 2015.","ista":"Alt J. 2015. The local semicircle law for random matrices with a fourfold symmetry. Journal of Mathematical Physics. 56(10), 103301.","ama":"Alt J. The local semicircle law for random matrices with a fourfold symmetry. Journal of Mathematical Physics. 2015;56(10). doi:10.1063/1.4932606"},"publication":"Journal of Mathematical Physics","issue":"10","abstract":[{"lang":"eng","text":"We consider real symmetric and complex Hermitian random matrices with the additional symmetry hxy = hN-y,N-x. The matrix elements are independent (up to the fourfold symmetry) and not necessarily identically distributed. This ensemble naturally arises as the Fourier transform of a Gaussian orthogonal ensemble. Italso occurs as the flip matrix model - an approximation of the two-dimensional Anderson model at small disorder. We show that the density of states converges to the Wigner semicircle law despite the new symmetry type. We also prove the local version of the semicircle law on the optimal scale."}],"type":"journal_article","oa_version":"Preprint","intvolume":" 56","title":"The local semicircle law for random matrices with a fourfold symmetry","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"1677","month":"10","language":[{"iso":"eng"}],"doi":"10.1063/1.4932606","project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/1506.04683","open_access":"1"}],"publist_id":"5472","ec_funded":1,"article_number":"103301","volume":56,"date_updated":"2023-09-07T12:38:08Z","date_created":"2018-12-11T11:53:25Z","related_material":{"record":[{"id":"149","status":"public","relation":"dissertation_contains"}]},"author":[{"full_name":"Alt, Johannes","last_name":"Alt","first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"}],"department":[{"_id":"LaEr"}],"publisher":"American Institute of Physics","publication_status":"published","year":"2015"},{"language":[{"iso":"eng"}],"doi":"10.1007/s11040-014-9163-4","project":[{"_id":"26450934-B435-11E9-9278-68D0E5697425","name":"NSERC Postdoctoral fellowship"},{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","external_id":{"arxiv":["1304.3862"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1304.3862","open_access":"1"}],"month":"12","volume":17,"date_created":"2018-12-11T11:54:45Z","date_updated":"2021-01-12T06:54:07Z","author":[{"first_name":"Christian","last_name":"Sadel","id":"4760E9F8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8255-3968","full_name":"Sadel, Christian"}],"publisher":"Springer","department":[{"_id":"LaEr"}],"publication_status":"published","year":"2014","ec_funded":1,"publist_id":"5168","date_published":"2014-12-17T00:00:00Z","page":"409 - 440","article_type":"original","citation":{"ista":"Sadel C. 2014. Absolutely continuous spectrum for random Schrödinger operators on the Fibonacci and similar Tree-strips. Mathematical Physics, Analysis and Geometry. 17(3–4), 409–440.","ieee":"C. Sadel, “Absolutely continuous spectrum for random Schrödinger operators on the Fibonacci and similar Tree-strips,” Mathematical Physics, Analysis and Geometry, vol. 17, no. 3–4. Springer, pp. 409–440, 2014.","apa":"Sadel, C. (2014). Absolutely continuous spectrum for random Schrödinger operators on the Fibonacci and similar Tree-strips. Mathematical Physics, Analysis and Geometry. Springer. https://doi.org/10.1007/s11040-014-9163-4","ama":"Sadel C. Absolutely continuous spectrum for random Schrödinger operators on the Fibonacci and similar Tree-strips. Mathematical Physics, Analysis and Geometry. 2014;17(3-4):409-440. doi:10.1007/s11040-014-9163-4","chicago":"Sadel, Christian. “Absolutely Continuous Spectrum for Random Schrödinger Operators on the Fibonacci and Similar Tree-Strips.” Mathematical Physics, Analysis and Geometry. Springer, 2014. https://doi.org/10.1007/s11040-014-9163-4.","mla":"Sadel, Christian. “Absolutely Continuous Spectrum for Random Schrödinger Operators on the Fibonacci and Similar Tree-Strips.” Mathematical Physics, Analysis and Geometry, vol. 17, no. 3–4, Springer, 2014, pp. 409–40, doi:10.1007/s11040-014-9163-4.","short":"C. Sadel, Mathematical Physics, Analysis and Geometry 17 (2014) 409–440."},"publication":"Mathematical Physics, Analysis and Geometry","article_processing_charge":"No","day":"17","scopus_import":1,"oa_version":"Preprint","intvolume":" 17","status":"public","title":"Absolutely continuous spectrum for random Schrödinger operators on the Fibonacci and similar Tree-strips","_id":"1926","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"3-4","abstract":[{"lang":"eng","text":"We consider cross products of finite graphs with a class of trees that have arbitrarily but finitely long line segments, such as the Fibonacci tree. Such cross products are called tree-strips. We prove that for small disorder random Schrödinger operators on such tree-strips have purely absolutely continuous spectrum in a certain set."}],"type":"journal_article"},{"date_published":"2014-11-01T00:00:00Z","citation":{"short":"P. Bourgade, L. Erdös, H. Yau, Communications in Mathematical Physics 332 (2014) 261–353.","mla":"Bourgade, Paul, et al. “Edge Universality of Beta Ensembles.” Communications in Mathematical Physics, vol. 332, no. 1, Springer, 2014, pp. 261–353, doi:10.1007/s00220-014-2120-z.","chicago":"Bourgade, Paul, László Erdös, and Horngtzer Yau. “Edge Universality of Beta Ensembles.” Communications in Mathematical Physics. Springer, 2014. https://doi.org/10.1007/s00220-014-2120-z.","ama":"Bourgade P, Erdös L, Yau H. Edge universality of beta ensembles. Communications in Mathematical Physics. 2014;332(1):261-353. doi:10.1007/s00220-014-2120-z","ieee":"P. Bourgade, L. Erdös, and H. Yau, “Edge universality of beta ensembles,” Communications in Mathematical Physics, vol. 332, no. 1. Springer, pp. 261–353, 2014.","apa":"Bourgade, P., Erdös, L., & Yau, H. (2014). Edge universality of beta ensembles. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-014-2120-z","ista":"Bourgade P, Erdös L, Yau H. 2014. Edge universality of beta ensembles. Communications in Mathematical Physics. 332(1), 261–353."},"publication":"Communications in Mathematical Physics","page":"261 - 353","day":"01","scopus_import":1,"oa_version":"Submitted Version","_id":"1937","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","intvolume":" 332","status":"public","title":"Edge universality of beta ensembles","issue":"1","abstract":[{"lang":"eng","text":"We prove the edge universality of the beta ensembles for any β ≥ 1, provided that the limiting spectrum is supported on a single interval, and the external potential is C4 and regular. We also prove that the edge universality holds for generalized Wigner matrices for all symmetry classes. Moreover, our results allow us to extend bulk universality for beta ensembles from analytic potentials to potentials in class C4."}],"type":"journal_article","doi":"10.1007/s00220-014-2120-z","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/1306.5728","open_access":"1"}],"project":[{"name":"Glutamaterge synaptische Übertragung und Plastizität in hippocampalen Mikroschaltkreisen","grant_number":"SFB-TR3-TP10B","_id":"25BDE9A4-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","month":"11","author":[{"first_name":"Paul","last_name":"Bourgade","full_name":"Bourgade, Paul"},{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"Yau, Horngtzer","first_name":"Horngtzer","last_name":"Yau"}],"volume":332,"date_created":"2018-12-11T11:54:48Z","date_updated":"2021-01-12T06:54:12Z","year":"2014","department":[{"_id":"LaEr"}],"publisher":"Springer","publication_status":"published","publist_id":"5158"},{"scopus_import":1,"day":"17","citation":{"chicago":"Erdös, László, and Dominik J Schröder. “Phase Transition in the Density of States of Quantum Spin Glasses.” Mathematical Physics, Analysis and Geometry. Springer, 2014. https://doi.org/10.1007/s11040-014-9164-3.","short":"L. Erdös, D.J. Schröder, Mathematical Physics, Analysis and Geometry 17 (2014) 441–464.","mla":"Erdös, László, and Dominik J. Schröder. “Phase Transition in the Density of States of Quantum Spin Glasses.” Mathematical Physics, Analysis and Geometry, vol. 17, no. 3–4, Springer, 2014, pp. 441–64, doi:10.1007/s11040-014-9164-3.","apa":"Erdös, L., & Schröder, D. J. (2014). Phase transition in the density of states of quantum spin glasses. Mathematical Physics, Analysis and Geometry. Springer. https://doi.org/10.1007/s11040-014-9164-3","ieee":"L. Erdös and D. J. Schröder, “Phase transition in the density of states of quantum spin glasses,” Mathematical Physics, Analysis and Geometry, vol. 17, no. 3–4. Springer, pp. 441–464, 2014.","ista":"Erdös L, Schröder DJ. 2014. Phase transition in the density of states of quantum spin glasses. Mathematical Physics, Analysis and Geometry. 17(3–4), 441–464.","ama":"Erdös L, Schröder DJ. Phase transition in the density of states of quantum spin glasses. Mathematical Physics, Analysis and Geometry. 2014;17(3-4):441-464. doi:10.1007/s11040-014-9164-3"},"publication":"Mathematical Physics, Analysis and Geometry","page":"441 - 464","date_published":"2014-12-17T00:00:00Z","type":"journal_article","issue":"3-4","abstract":[{"lang":"eng","text":"We prove that the empirical density of states of quantum spin glasses on arbitrary graphs converges to a normal distribution as long as the maximal degree is negligible compared with the total number of edges. This extends the recent results of Keating et al. (2014) that were proved for graphs with bounded chromatic number and with symmetric coupling distribution. Furthermore, we generalise the result to arbitrary hypergraphs. We test the optimality of our condition on the maximal degree for p-uniform hypergraphs that correspond to p-spin glass Hamiltonians acting on n distinguishable spin- 1/2 particles. At the critical threshold p = n1/2 we find a sharp classical-quantum phase transition between the normal distribution and the Wigner semicircle law. The former is characteristic to classical systems with commuting variables, while the latter is a signature of noncommutative random matrix theory."}],"_id":"2019","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","intvolume":" 17","status":"public","title":"Phase transition in the density of states of quantum spin glasses","oa_version":"Submitted Version","month":"12","main_file_link":[{"url":"http://arxiv.org/abs/1407.1552","open_access":"1"}],"oa":1,"project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"}],"quality_controlled":"1","doi":"10.1007/s11040-014-9164-3","language":[{"iso":"eng"}],"publist_id":"5053","ec_funded":1,"year":"2014","department":[{"_id":"LaEr"}],"publisher":"Springer","publication_status":"published","author":[{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"Schröder, Dominik J","last_name":"Schröder","first_name":"Dominik J"}],"volume":17,"date_created":"2018-12-11T11:55:15Z","date_updated":"2021-01-12T06:54:45Z"},{"has_accepted_license":"1","day":"09","scopus_import":1,"date_published":"2014-06-09T00:00:00Z","citation":{"ama":"Ajanki OH, Erdös L, Krüger TH. Local semicircle law with imprimitive variance matrix. Electronic Communications in Probability. 2014;19. doi:10.1214/ECP.v19-3121","ista":"Ajanki OH, Erdös L, Krüger TH. 2014. Local semicircle law with imprimitive variance matrix. Electronic Communications in Probability. 19.","ieee":"O. H. Ajanki, L. Erdös, and T. H. Krüger, “Local semicircle law with imprimitive variance matrix,” Electronic Communications in Probability, vol. 19. Institute of Mathematical Statistics, 2014.","apa":"Ajanki, O. H., Erdös, L., & Krüger, T. H. (2014). Local semicircle law with imprimitive variance matrix. Electronic Communications in Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/ECP.v19-3121","mla":"Ajanki, Oskari H., et al. “Local Semicircle Law with Imprimitive Variance Matrix.” Electronic Communications in Probability, vol. 19, Institute of Mathematical Statistics, 2014, doi:10.1214/ECP.v19-3121.","short":"O.H. Ajanki, L. Erdös, T.H. Krüger, Electronic Communications in Probability 19 (2014).","chicago":"Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Local Semicircle Law with Imprimitive Variance Matrix.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2014. https://doi.org/10.1214/ECP.v19-3121."},"publication":"Electronic Communications in Probability","abstract":[{"lang":"eng","text":"We extend the proof of the local semicircle law for generalized Wigner matrices given in MR3068390 to the case when the matrix of variances has an eigenvalue -1. In particular, this result provides a short proof of the optimal local Marchenko-Pastur law at the hard edge (i.e. around zero) for sample covariance matrices X*X, where the variances of the entries of X may vary."}],"type":"journal_article","oa_version":"Published Version","file":[{"checksum":"bd8a041c76d62fe820bf73ff13ce7d1b","date_created":"2018-12-12T10:09:06Z","date_updated":"2020-07-14T12:45:31Z","file_id":"4729","relation":"main_file","creator":"system","file_size":327322,"content_type":"application/pdf","access_level":"open_access","file_name":"IST-2016-426-v1+1_3121-17518-1-PB.pdf"}],"pubrep_id":"426","intvolume":" 19","status":"public","title":"Local semicircle law with imprimitive variance matrix","ddc":["570"],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","_id":"2179","month":"06","language":[{"iso":"eng"}],"doi":"10.1214/ECP.v19-3121","quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"publist_id":"4803","file_date_updated":"2020-07-14T12:45:31Z","volume":19,"date_updated":"2021-01-12T06:55:48Z","date_created":"2018-12-11T11:56:10Z","author":[{"last_name":"Ajanki","first_name":"Oskari H","id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87","full_name":"Ajanki, Oskari H"},{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","last_name":"Krüger","first_name":"Torben H"}],"publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"publication_status":"published","year":"2014"},{"day":"15","has_accepted_license":"1","date_published":"2014-03-15T00:00:00Z","publication":"Electronic Journal of Probability","citation":{"ama":"Bloemendal A, Erdös L, Knowles A, Yau H, Yin J. Isotropic local laws for sample covariance and generalized Wigner matrices. Electronic Journal of Probability. 2014;19. doi:10.1214/EJP.v19-3054","ista":"Bloemendal A, Erdös L, Knowles A, Yau H, Yin J. 2014. Isotropic local laws for sample covariance and generalized Wigner matrices. Electronic Journal of Probability. 19, 33.","apa":"Bloemendal, A., Erdös, L., Knowles, A., Yau, H., & Yin, J. (2014). Isotropic local laws for sample covariance and generalized Wigner matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/EJP.v19-3054","ieee":"A. Bloemendal, L. Erdös, A. Knowles, H. Yau, and J. Yin, “Isotropic local laws for sample covariance and generalized Wigner matrices,” Electronic Journal of Probability, vol. 19. Institute of Mathematical Statistics, 2014.","mla":"Bloemendal, Alex, et al. “Isotropic Local Laws for Sample Covariance and Generalized Wigner Matrices.” Electronic Journal of Probability, vol. 19, 33, Institute of Mathematical Statistics, 2014, doi:10.1214/EJP.v19-3054.","short":"A. Bloemendal, L. Erdös, A. Knowles, H. Yau, J. Yin, Electronic Journal of Probability 19 (2014).","chicago":"Bloemendal, Alex, László Erdös, Antti Knowles, Horng Yau, and Jun Yin. “Isotropic Local Laws for Sample Covariance and Generalized Wigner Matrices.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2014. https://doi.org/10.1214/EJP.v19-3054."},"abstract":[{"lang":"eng","text":"We consider sample covariance matrices of the form X∗X, where X is an M×N matrix with independent random entries. We prove the isotropic local Marchenko-Pastur law, i.e. we prove that the resolvent (X∗X−z)−1 converges to a multiple of the identity in the sense of quadratic forms. More precisely, we establish sharp high-probability bounds on the quantity ⟨v,(X∗X−z)−1w⟩−⟨v,w⟩m(z), where m is the Stieltjes transform of the Marchenko-Pastur law and v,w∈CN. We require the logarithms of the dimensions M and N to be comparable. Our result holds down to scales Iz≥N−1+ε and throughout the entire spectrum away from 0. We also prove analogous results for generalized Wigner matrices.\r\n"}],"type":"journal_article","file":[{"file_id":"5055","relation":"main_file","date_updated":"2020-07-14T12:45:34Z","date_created":"2018-12-12T10:14:06Z","checksum":"7eb297ff367a2ee73b21b6dd1e1948e4","file_name":"IST-2016-427-v1+1_3054-16624-4-PB.pdf","access_level":"open_access","creator":"system","file_size":810150,"content_type":"application/pdf"}],"oa_version":"Published Version","pubrep_id":"427","status":"public","title":"Isotropic local laws for sample covariance and generalized Wigner matrices","ddc":["510"],"intvolume":" 19","_id":"2225","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"03","publication_identifier":{"issn":["10836489"]},"language":[{"iso":"eng"}],"doi":"10.1214/EJP.v19-3054","quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"file_date_updated":"2020-07-14T12:45:34Z","publist_id":"4739","ec_funded":1,"article_number":"33","date_created":"2018-12-11T11:56:25Z","date_updated":"2021-01-12T06:56:07Z","volume":19,"author":[{"first_name":"Alex","last_name":"Bloemendal","full_name":"Bloemendal, Alex"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"Erdös, László"},{"full_name":"Knowles, Antti","first_name":"Antti","last_name":"Knowles"},{"full_name":"Yau, Horng","last_name":"Yau","first_name":"Horng"},{"full_name":"Yin, Jun","last_name":"Yin","first_name":"Jun"}],"publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","year":"2014"},{"month":"04","day":"01","scopus_import":1,"language":[{"iso":"eng"}],"date_published":"2014-04-01T00:00:00Z","doi":"10.1215/00127094-2649752","quality_controlled":"1","page":"1127 - 1190","publication":"Duke Mathematical Journal","main_file_link":[{"url":"http://arxiv.org/abs/1104.2272","open_access":"1"}],"oa":1,"citation":{"ieee":"L. Erdös, P. Bourgade, and H. Yau, “Universality of general β-ensembles,” Duke Mathematical Journal, vol. 163, no. 6. Duke University Press, pp. 1127–1190, 2014.","apa":"Erdös, L., Bourgade, P., & Yau, H. (2014). Universality of general β-ensembles. Duke Mathematical Journal. Duke University Press. https://doi.org/10.1215/00127094-2649752","ista":"Erdös L, Bourgade P, Yau H. 2014. Universality of general β-ensembles. Duke Mathematical Journal. 163(6), 1127–1190.","ama":"Erdös L, Bourgade P, Yau H. Universality of general β-ensembles. Duke Mathematical Journal. 2014;163(6):1127-1190. doi:10.1215/00127094-2649752","chicago":"Erdös, László, Paul Bourgade, and Horng Yau. “Universality of General β-Ensembles.” Duke Mathematical Journal. Duke University Press, 2014. https://doi.org/10.1215/00127094-2649752.","short":"L. Erdös, P. Bourgade, H. Yau, Duke Mathematical Journal 163 (2014) 1127–1190.","mla":"Erdös, László, et al. “Universality of General β-Ensembles.” Duke Mathematical Journal, vol. 163, no. 6, Duke University Press, 2014, pp. 1127–90, doi:10.1215/00127094-2649752."},"abstract":[{"text":"We prove the universality of the β-ensembles with convex analytic potentials and for any β >\r\n0, i.e. we show that the spacing distributions of log-gases at any inverse temperature β coincide with those of the Gaussian β-ensembles.","lang":"eng"}],"issue":"6","publist_id":"4197","type":"journal_article","date_created":"2018-12-11T11:59:08Z","date_updated":"2021-01-12T06:59:07Z","oa_version":"Preprint","volume":163,"author":[{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"last_name":"Bourgade","first_name":"Paul","full_name":"Bourgade, Paul"},{"last_name":"Yau","first_name":"Horng","full_name":"Yau, Horng"}],"status":"public","publication_status":"published","title":"Universality of general β-ensembles","intvolume":" 163","publisher":"Duke University Press","department":[{"_id":"LaEr"}],"year":"2014","_id":"2699","user_id":"3FFCCD3A-F248-11E8-B48F-1D18A9856A87"},{"month":"08","language":[{"iso":"eng"}],"conference":{"name":"ICM: International Congress of Mathematicians","location":"Seoul, Korea","start_date":"2014-08-13","end_date":"2014-08-21"},"quality_controlled":"1","project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"main_file_link":[{"url":"http://arxiv.org/abs/1407.5752","open_access":"1"}],"oa":1,"publist_id":"5670","ec_funded":1,"date_updated":"2023-10-17T11:12:55Z","date_created":"2018-12-11T11:52:25Z","volume":3,"author":[{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"}],"publication_status":"published","publisher":"International Congress of Mathematicians","department":[{"_id":"LaEr"}],"acknowledgement":"The author is partially supported by SFB-TR 12 Grant of the German Research Council.","year":"2014","day":"01","article_processing_charge":"No","scopus_import":"1","date_published":"2014-08-01T00:00:00Z","page":"214 - 236","publication":"Proceedings of the International Congress of Mathematicians","citation":{"mla":"Erdös, László. “Random Matrices, Log-Gases and Hölder Regularity.” Proceedings of the International Congress of Mathematicians, vol. 3, International Congress of Mathematicians, 2014, pp. 214–36.","short":"L. Erdös, in:, Proceedings of the International Congress of Mathematicians, International Congress of Mathematicians, 2014, pp. 214–236.","chicago":"Erdös, László. “Random Matrices, Log-Gases and Hölder Regularity.” In Proceedings of the International Congress of Mathematicians, 3:214–36. International Congress of Mathematicians, 2014.","ama":"Erdös L. Random matrices, log-gases and Hölder regularity. In: Proceedings of the International Congress of Mathematicians. Vol 3. International Congress of Mathematicians; 2014:214-236.","ista":"Erdös L. 2014. Random matrices, log-gases and Hölder regularity. Proceedings of the International Congress of Mathematicians. ICM: International Congress of Mathematicians vol. 3, 214–236.","apa":"Erdös, L. (2014). Random matrices, log-gases and Hölder regularity. In Proceedings of the International Congress of Mathematicians (Vol. 3, pp. 214–236). Seoul, Korea: International Congress of Mathematicians.","ieee":"L. Erdös, “Random matrices, log-gases and Hölder regularity,” in Proceedings of the International Congress of Mathematicians, Seoul, Korea, 2014, vol. 3, pp. 214–236."},"abstract":[{"lang":"eng","text":"The Wigner-Dyson-Gaudin-Mehta conjecture asserts that the local eigenvalue statistics of large real and complex Hermitian matrices with independent, identically distributed entries are universal in a sense that they depend only on the symmetry class of the matrix and otherwise are independent of the details of the distribution. We present the recent solution to this half-century old conjecture. We explain how stochastic tools, such as the Dyson Brownian motion, and PDE ideas, such as De Giorgi-Nash-Moser regularity theory, were combined in the solution. We also show related results for log-gases that represent a universal model for strongly correlated systems. Finally, in the spirit of Wigner’s original vision, we discuss the extensions of these universality results to more realistic physical systems such as random band matrices."}],"type":"conference","oa_version":"Submitted Version","title":"Random matrices, log-gases and Hölder regularity","status":"public","intvolume":" 3","_id":"1507","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"author":[{"full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"full_name":"Fournais, Søren","first_name":"Søren","last_name":"Fournais"},{"first_name":"Jan","last_name":"Solovej","full_name":"Solovej, Jan"}],"oa_version":"Preprint","volume":15,"date_created":"2018-12-11T11:59:07Z","date_updated":"2021-01-12T06:59:07Z","_id":"2698","year":"2013","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"LaEr"}],"publisher":"European Mathematical Society","intvolume":" 15","status":"public","title":"Stability and semiclassics in self-generated fields","publication_status":"published","issue":"6","publist_id":"4198","abstract":[{"lang":"eng","text":"We consider non-interacting particles subject to a fixed external potential V and a self-generated magnetic field B. The total energy includes the field energy β∫B2 and we minimize over all particle states and magnetic fields. In the case of spin-1/2 particles this minimization leads to the coupled Maxwell-Pauli system. The parameter β tunes the coupling strength between the field and the particles and it effectively determines the strength of the field. We investigate the stability and the semiclassical asymptotics, h→0, of the total ground state energy E(β,h,V). The relevant parameter measuring the field strength in the semiclassical limit is κ=βh. We are not able to give the exact leading order semiclassical asymptotics uniformly in κ or even for fixed κ. We do however give upper and lower bounds on E with almost matching dependence on κ. In the simultaneous limit h→0 and κ→∞ we show that the standard non-magnetic Weyl asymptotics holds. The same result also holds for the spinless case, i.e. where the Pauli operator is replaced by the Schrödinger operator."}],"type":"journal_article","doi":"10.4171/JEMS/416","date_published":"2013-10-16T00:00:00Z","language":[{"iso":"eng"}],"citation":{"ama":"Erdös L, Fournais S, Solovej J. Stability and semiclassics in self-generated fields. Journal of the European Mathematical Society. 2013;15(6):2093-2113. doi:10.4171/JEMS/416","ista":"Erdös L, Fournais S, Solovej J. 2013. Stability and semiclassics in self-generated fields. Journal of the European Mathematical Society. 15(6), 2093–2113.","apa":"Erdös, L., Fournais, S., & Solovej, J. (2013). Stability and semiclassics in self-generated fields. Journal of the European Mathematical Society. European Mathematical Society. https://doi.org/10.4171/JEMS/416","ieee":"L. Erdös, S. Fournais, and J. Solovej, “Stability and semiclassics in self-generated fields,” Journal of the European Mathematical Society, vol. 15, no. 6. European Mathematical Society, pp. 2093–2113, 2013.","mla":"Erdös, László, et al. “Stability and Semiclassics in Self-Generated Fields.” Journal of the European Mathematical Society, vol. 15, no. 6, European Mathematical Society, 2013, pp. 2093–113, doi:10.4171/JEMS/416.","short":"L. Erdös, S. Fournais, J. Solovej, Journal of the European Mathematical Society 15 (2013) 2093–2113.","chicago":"Erdös, László, Søren Fournais, and Jan Solovej. “Stability and Semiclassics in Self-Generated Fields.” Journal of the European Mathematical Society. European Mathematical Society, 2013. https://doi.org/10.4171/JEMS/416."},"external_id":{"arxiv":["1105.0506"]},"main_file_link":[{"url":"http://arxiv.org/abs/1105.0506","open_access":"1"}],"oa":1,"publication":"Journal of the European Mathematical Society","page":"2093 - 2113","quality_controlled":"1","day":"16","month":"10"},{"scopus_import":1,"day":"18","citation":{"short":"L. Erdös, B. Farrell, Journal of Statistical Physics 152 (2013) 1003–1032.","mla":"Erdös, László, and Brendan Farrell. “Local Eigenvalue Density for General MANOVA Matrices.” Journal of Statistical Physics, vol. 152, no. 6, Springer, 2013, pp. 1003–32, doi:10.1007/s10955-013-0807-8.","chicago":"Erdös, László, and Brendan Farrell. “Local Eigenvalue Density for General MANOVA Matrices.” Journal of Statistical Physics. Springer, 2013. https://doi.org/10.1007/s10955-013-0807-8.","ama":"Erdös L, Farrell B. Local eigenvalue density for general MANOVA matrices. Journal of Statistical Physics. 2013;152(6):1003-1032. doi:10.1007/s10955-013-0807-8","apa":"Erdös, L., & Farrell, B. (2013). Local eigenvalue density for general MANOVA matrices. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-013-0807-8","ieee":"L. Erdös and B. Farrell, “Local eigenvalue density for general MANOVA matrices,” Journal of Statistical Physics, vol. 152, no. 6. Springer, pp. 1003–1032, 2013.","ista":"Erdös L, Farrell B. 2013. Local eigenvalue density for general MANOVA matrices. Journal of Statistical Physics. 152(6), 1003–1032."},"publication":"Journal of Statistical Physics","page":"1003 - 1032","date_published":"2013-07-18T00:00:00Z","type":"journal_article","issue":"6","abstract":[{"lang":"eng","text":"We consider random n×n matrices of the form (XX*+YY*)^{-1/2}YY*(XX*+YY*)^{-1/2}, where X and Y have independent entries with zero mean and variance one. These matrices are the natural generalization of the Gaussian case, which are known as MANOVA matrices and which have joint eigenvalue density given by the third classical ensemble, the Jacobi ensemble. We show that, away from the spectral edge, the eigenvalue density converges to the limiting density of the Jacobi ensemble even on the shortest possible scales of order 1/n (up to log n factors). This result is the analogue of the local Wigner semicircle law and the local Marchenko-Pastur law for general MANOVA matrices."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2782","intvolume":" 152","title":"Local eigenvalue density for general MANOVA matrices","status":"public","oa_version":"Preprint","month":"07","external_id":{"arxiv":["1207.0031"]},"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1207.0031"}],"oa":1,"quality_controlled":"1","doi":"10.1007/s10955-013-0807-8","language":[{"iso":"eng"}],"publist_id":"4107","year":"2013","publisher":"Springer","department":[{"_id":"LaEr"}],"publication_status":"published","author":[{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Farrell","first_name":"Brendan","full_name":"Farrell, Brendan"}],"volume":152,"date_updated":"2021-01-12T06:59:41Z","date_created":"2018-12-11T11:59:34Z"},{"file_date_updated":"2020-07-14T12:45:50Z","publist_id":"3962","date_updated":"2021-01-12T07:00:06Z","date_created":"2018-12-11T11:59:51Z","volume":18,"author":[{"full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"first_name":"Antti","last_name":"Knowles","full_name":"Knowles, Antti"},{"full_name":"Yau, Horng","last_name":"Yau","first_name":"Horng"},{"full_name":"Yin, Jun","last_name":"Yin","first_name":"Jun"}],"publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","year":"2013","month":"05","language":[{"iso":"eng"}],"doi":"10.1214/EJP.v18-2473","quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"abstract":[{"lang":"eng","text":"We consider a general class of N × N random matrices whose entries hij are independent up to a symmetry constraint, but not necessarily identically distributed. Our main result is a local semicircle law which improves previous results [17] both in the bulk and at the edge. The error bounds are given in terms of the basic small parameter of the model, maxi,j E|hij|2. As a consequence, we prove the universality of the local n-point correlation functions in the bulk spectrum for a class of matrices whose entries do not have comparable variances, including random band matrices with band width W ≫N1-εn with some εn > 0 and with a negligible mean-field component. In addition, we provide a coherent and pedagogical proof of the local semicircle law, streamlining and strengthening previous arguments from [17, 19, 6]."}],"issue":"59","type":"journal_article","oa_version":"Published Version","file":[{"creator":"system","content_type":"application/pdf","file_size":651497,"file_name":"IST-2016-406-v1+1_2473-13759-1-PB.pdf","access_level":"open_access","date_created":"2018-12-12T10:15:46Z","date_updated":"2020-07-14T12:45:50Z","checksum":"aac9e52a00cb2f5149dc9e362b5ccf44","file_id":"5169","relation":"main_file"}],"pubrep_id":"406","ddc":["530"],"status":"public","title":"The local semicircle law for a general class of random matrices","intvolume":" 18","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"2837","day":"29","has_accepted_license":"1","scopus_import":1,"date_published":"2013-05-29T00:00:00Z","page":"1-58","publication":"Electronic Journal of Probability","citation":{"ieee":"L. Erdös, A. Knowles, H. Yau, and J. Yin, “The local semicircle law for a general class of random matrices,” Electronic Journal of Probability, vol. 18, no. 59. Institute of Mathematical Statistics, pp. 1–58, 2013.","apa":"Erdös, L., Knowles, A., Yau, H., & Yin, J. (2013). The local semicircle law for a general class of random matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/EJP.v18-2473","ista":"Erdös L, Knowles A, Yau H, Yin J. 2013. The local semicircle law for a general class of random matrices. Electronic Journal of Probability. 18(59), 1–58.","ama":"Erdös L, Knowles A, Yau H, Yin J. The local semicircle law for a general class of random matrices. Electronic Journal of Probability. 2013;18(59):1-58. doi:10.1214/EJP.v18-2473","chicago":"Erdös, László, Antti Knowles, Horng Yau, and Jun Yin. “The Local Semicircle Law for a General Class of Random Matrices.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2013. https://doi.org/10.1214/EJP.v18-2473.","short":"L. Erdös, A. Knowles, H. Yau, J. Yin, Electronic Journal of Probability 18 (2013) 1–58.","mla":"Erdös, László, et al. “The Local Semicircle Law for a General Class of Random Matrices.” Electronic Journal of Probability, vol. 18, no. 59, Institute of Mathematical Statistics, 2013, pp. 1–58, doi:10.1214/EJP.v18-2473."}}]