[{"status":"public","main_file_link":[{"url":"https://doi.org/10.1007/s00220-019-03657-4","open_access":"1"}],"type":"journal_article","publication":"Communications in Mathematical Physics","external_id":{"arxiv":["1809.03971"]},"page":"50","day":"28","title":"Cusp universality for random matrices I: Local law and the complex hermitian case","citation":{"mla":"Erdös, László, et al. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” *Communications in Mathematical Physics*, Springer Nature, 2020, p. 50, 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*, 2020, 50. https://doi.org/10.1007/s00220-019-03657-4.","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., 50.","ama":"Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices I: Local law and the complex hermitian case. *Communications in Mathematical Physics*. 2020:50. doi:10.1007/s00220-019-03657-4","apa":"Erdös, L., Krüger, T. H., & Schröder, D. J. (2020). Cusp universality for random matrices I: Local law and the complex hermitian case. *Communications in Mathematical Physics*, 50. https://doi.org/10.1007/s00220-019-03657-4","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics (2020) 50.","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*, p. 50, 2020."},"oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","related_material":{"record":[{"id":"6179","relation":"dissertation_contains","status":"public"}]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"LaEr"}],"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"oa":1,"year":"2020","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"article_type":"original","date_published":"2020-04-28T00:00:00Z","author":[{"orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H","full_name":"Krüger, Torben H","last_name":"Krüger"},{"full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","last_name":"Schröder"}],"publisher":"Springer Nature","language":[{"iso":"eng"}],"publication_status":"epub_ahead","date_updated":"2020-05-11T11:24:32Z","_id":"6185","quality_controlled":"1","date_created":"2019-03-28T10:21:15Z","abstract":[{"lang":"eng","text":"For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are universal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner–Dyson–Mehta universality conjecture for the last remaining universality type in the complex Hermitian class. Our analysis holds not only for exact cusps, but approximate cusps as well, where an extended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp for both symmetry classes. This result is also the key input in the companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where the cusp universality for real symmetric Wigner-type matrices is proven. The novel cusp fluctuation mechanism is also essential for the recent results on the spectral radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian edge universality (Cipolloni et al. in Edge universality for non-Hermitian random matrices, 2019. arXiv:1908.00969)."}],"doi":"10.1007/s00220-019-03657-4","month":"04"},{"publication":"Journal of Functional Analysis","external_id":{"arxiv":["1804.11340"]},"publisher":"Elsevier","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1804.11340","open_access":"1"}],"author":[{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László"},{"full_name":"Krüger, Torben H","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","last_name":"Krüger"},{"first_name":"Yuriy","orcid":"0000-0002-7327-856X","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","full_name":"Nemish, Yuriy","last_name":"Nemish"}],"type":"journal_article","publication_status":"inpress","date_published":"2020-02-10T00:00:00Z","article_type":"original","year":"2020","status":"public","oa_version":"Preprint","date_created":"2020-02-23T23:00:36Z","citation":{"chicago":"Erdös, László, Torben H Krüger, and Yuriy Nemish. “Local Laws for Polynomials of Wigner Matrices.” *Journal of Functional Analysis*, n.d., 108507. https://doi.org/10.1016/j.jfa.2020.108507.","mla":"Erdös, László, et al. “Local Laws for Polynomials of Wigner Matrices.” *Journal of Functional Analysis*, Elsevier, p. 108507, doi:10.1016/j.jfa.2020.108507.","ista":"Erdös L, Krüger TH, Nemish Y. Local laws for polynomials of Wigner matrices. Journal of Functional Analysis., 108507.","ieee":"L. Erdös, T. H. Krüger, and Y. Nemish, “Local laws for polynomials of Wigner matrices,” *Journal of Functional Analysis*, p. 108507.","ama":"Erdös L, Krüger TH, Nemish Y. Local laws for polynomials of Wigner matrices. *Journal of Functional Analysis*.:108507. doi:10.1016/j.jfa.2020.108507","short":"L. Erdös, T.H. Krüger, Y. Nemish, Journal of Functional Analysis (n.d.) 108507.","apa":"Erdös, L., Krüger, T. H., & Nemish, Y. (n.d.). Local laws for polynomials of Wigner matrices. *Journal of Functional Analysis*, 108507. https://doi.org/10.1016/j.jfa.2020.108507"},"article_processing_charge":"No","article_number":"108507","oa":1,"publication_identifier":{"issn":["00221236"],"eissn":["10960783"]},"abstract":[{"lang":"eng","text":"We consider general self-adjoint polynomials in several independent random matrices whose entries are centered and have the same variance. We show that under certain conditions the local law holds up to the optimal scale, i.e., the eigenvalue density on scales just above the eigenvalue spacing follows the global density of states which is determined by free probability theory. We prove that these conditions hold for general homogeneous polynomials of degree two and for symmetrized products of independent matrices with i.i.d. entries, thus establishing the optimal bulk local law for these classes of ensembles. In particular, we generalize a similar result of Anderson for anticommutator. For more general polynomials our conditions are effectively checkable numerically."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.1016/j.jfa.2020.108507","department":[{"_id":"LaEr"}],"month":"02","date_updated":"2020-02-24T13:49:29Z","day":"10","title":"Local laws for polynomials of Wigner matrices","quality_controlled":"1","_id":"7512"},{"oa_version":"Preprint","date_created":"2020-03-25T15:57:48Z","citation":{"mla":"Pitrik, Jozsef, and Daniel Virosztek. “Quantum Hellinger Distances Revisited.” *Letters in Mathematical Physics*, Springer Nature, 2020, doi:10.1007/s11005-020-01282-0.","chicago":"Pitrik, Jozsef, and Daniel Virosztek. “Quantum Hellinger Distances Revisited.” *Letters in Mathematical Physics*, 2020. https://doi.org/10.1007/s11005-020-01282-0.","apa":"Pitrik, J., & Virosztek, D. (2020). Quantum Hellinger distances revisited. *Letters in Mathematical Physics*. https://doi.org/10.1007/s11005-020-01282-0","ama":"Pitrik J, Virosztek D. Quantum Hellinger distances revisited. *Letters in Mathematical Physics*. 2020. doi:10.1007/s11005-020-01282-0","ieee":"J. Pitrik and D. Virosztek, “Quantum Hellinger distances revisited,” *Letters in Mathematical Physics*, 2020.","short":"J. Pitrik, D. Virosztek, Letters in Mathematical Physics (2020).","ista":"Pitrik J, Virosztek D. 2020. Quantum Hellinger distances revisited. Letters in Mathematical Physics."},"article_processing_charge":"No","oa":1,"publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","text":"This short note aims to study quantum Hellinger distances investigated recently by Bhatia et al. (Lett Math Phys 109:1777–1804, 2019) with a particular emphasis on barycenters. We introduce the family of generalized quantum Hellinger divergences that are of the form ϕ(A,B)=Tr((1−c)A+cB−AσB), where σ is an arbitrary Kubo–Ando mean, and c∈(0,1) is the weight of σ. We note that these divergences belong to the family of maximal quantum f-divergences, and hence are jointly convex, and satisfy the data processing inequality. We derive a characterization of the barycenter of finitely many positive definite operators for these generalized quantum Hellinger divergences. We note that the characterization of the barycenter as the weighted multivariate 1/2-power mean, that was claimed in Bhatia et al. (2019), is true in the case of commuting operators, but it is not correct in the general case. "}],"month":"03","department":[{"_id":"LaEr"}],"doi":"10.1007/s11005-020-01282-0","date_updated":"2020-03-27T11:47:51Z","day":"10","title":"Quantum Hellinger distances revisited","quality_controlled":"1","_id":"7618","publisher":"Springer Nature","publication":"Letters in Mathematical Physics","external_id":{"arxiv":["1903.10455"]},"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.10455"}],"author":[{"full_name":"Pitrik, Jozsef","first_name":"Jozsef","last_name":"Pitrik"},{"last_name":"Virosztek","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel","full_name":"Virosztek, Daniel"}],"type":"journal_article","publication_status":"epub_ahead","date_published":"2020-03-10T00:00:00Z","project":[{"_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability"},{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"article_type":"original","year":"2020","status":"public"},{"publication_status":"published","language":[{"iso":"eng"}],"publisher":"Project Euclid","author":[{"last_name":"Alt","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","first_name":"Johannes","full_name":"Alt, Johannes"},{"first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös"},{"full_name":"Krüger, Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H","last_name":"Krüger"},{"full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","last_name":"Schröder"}],"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"date_published":"2020-03-01T00:00:00Z","article_type":"original","year":"2020","month":"03","abstract":[{"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.","lang":"eng"}],"date_created":"2019-03-28T09:20:08Z","volume":48,"_id":"6184","quality_controlled":"1","date_updated":"2020-05-12T11:16:24Z","page":"963-1001","external_id":{"arxiv":["1804.07744"]},"publication":"Annals of Probability","type":"journal_article","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.07744"}],"status":"public","issue":"2","intvolume":" 48","oa":1,"department":[{"_id":"LaEr"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"record":[{"status":"public","id":"149","relation":"dissertation_contains"},{"id":"6179","relation":"dissertation_contains","status":"public"}]},"article_processing_charge":"No","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.","apa":"Alt, J., Erdös, L., Krüger, T. H., & Schröder, D. J. (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, pp. 963–1001, 2020.","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.","short":"J. Alt, L. Erdös, T.H. Krüger, D.J. Schröder, Annals of Probability 48 (2020) 963–1001.","mla":"Alt, Johannes, et al. “Correlated Random Matrices: Band Rigidity and Edge Universality.” *Annals of Probability*, vol. 48, no. 2, Project Euclid, 2020, pp. 963–1001.","chicago":"Alt, Johannes, László Erdös, Torben H Krüger, and Dominik J Schröder. “Correlated Random Matrices: Band Rigidity and Edge Universality.” *Annals of Probability* 48, no. 2 (2020): 963–1001."},"oa_version":"Preprint","title":"Correlated random matrices: Band rigidity and edge universality","day":"01"},{"article_processing_charge":"No","citation":{"mla":"Geher, Gyorgy Pal, et al. “Isometric Study of Wasserstein Spaces - the Real Line.” *Transactions of the American Mathematical Society*, American Mathematical Society, 2020, p. 32, doi:10.1090/tran/8113.","chicago":"Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Isometric Study of Wasserstein Spaces - the Real Line.” *Transactions of the American Mathematical Society*, 2020, 32. https://doi.org/10.1090/tran/8113.","ista":"Geher GP, Titkos T, Virosztek D. 2020. Isometric study of Wasserstein spaces - the real line. Transactions of the American Mathematical Society., 32.","short":"G.P. Geher, T. Titkos, D. Virosztek, Transactions of the American Mathematical Society (2020) 32.","ieee":"G. P. Geher, T. Titkos, and D. Virosztek, “Isometric study of Wasserstein spaces - the real line,” *Transactions of the American Mathematical Society*, p. 32, 2020.","ama":"Geher GP, Titkos T, Virosztek D. Isometric study of Wasserstein spaces - the real line. *Transactions of the American Mathematical Society*. 2020:32. doi:10.1090/tran/8113","apa":"Geher, G. P., Titkos, T., & Virosztek, D. (2020). Isometric study of Wasserstein spaces - the real line. *Transactions of the American Mathematical Society*, 32. https://doi.org/10.1090/tran/8113"},"oa_version":"Preprint","oa":1,"publication_identifier":{"issn":["00029947"],"eissn":["10886850"]},"department":[{"_id":"LaEr"}],"user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","day":"26","title":"Isometric study of Wasserstein spaces - the real line","publication":"Transactions of the American Mathematical Society","external_id":{"arxiv":["2002.00859"]},"type":"journal_article","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2002.00859"}],"page":"32","ddc":["515"],"status":"public","date_created":"2020-01-29T10:20:46Z","month":"05","doi":"10.1090/tran/8113","abstract":[{"lang":"eng","text":"Recently Kloeckner described the structure of the isometry group of the quadratic Wasserstein space W_2(R^n). It turned out that the case of the real line is exceptional in the sense that there exists an exotic isometry flow. Following this line of investigation, we compute Isom(W_p(R)), the isometry group of the Wasserstein space\r\nW_p(R) for all p \\in [1,\\infty) \\setminus {2}. We show that W_2(R) is also exceptional regarding the\r\nparameter p: W_p(R) is isometrically rigid if and only if p is not equal to 2. Regarding the underlying\r\nspace, we prove that the exceptionality of p = 2 disappears if we replace R by the compact\r\ninterval [0,1]. Surprisingly, in that case, W_p([0,1]) is isometrically rigid if and only if\r\np is not equal to 1. Moreover, W_1([0,1]) admits isometries that split mass, and Isom(W_1([0,1]))\r\ncannot be embedded into Isom(W_1(R))."}],"date_updated":"2020-07-07T09:01:12Z","_id":"7389","quality_controlled":"1","language":[{"iso":"eng"}],"publisher":"American Mathematical Society","author":[{"first_name":"Gyorgy Pal","full_name":"Geher, Gyorgy Pal","last_name":"Geher"},{"first_name":"Tamas","full_name":"Titkos, Tamas","last_name":"Titkos"},{"first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","full_name":"Virosztek, Daniel","last_name":"Virosztek"}],"publication_status":"epub_ahead","keyword":["Wasserstein space","isometric embeddings","isometric rigidity","exotic isometry flow"],"project":[{"_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability"}],"article_type":"original","date_published":"2020-05-26T00:00:00Z","year":"2020"}]