[{"publisher":"Springer Nature","quality_controlled":"1","oa":1,"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.","page":"2039-2052","date_published":"2020-08-01T00:00:00Z","doi":"10.1007/s11005-020-01282-0","date_created":"2020-03-25T15:57:48Z","isi":1,"year":"2020","day":"01","publication":"Letters in Mathematical Physics","project":[{"grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability","_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"author":[{"last_name":"Pitrik","full_name":"Pitrik, Jozsef","first_name":"Jozsef"},{"last_name":"Virosztek","full_name":"Virosztek, Daniel","orcid":"0000-0003-1109-5511","first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","external_id":{"isi":["000551556000002"],"arxiv":["1903.10455"]},"title":"Quantum Hellinger distances revisited","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.","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","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","ieee":"J. Pitrik and D. Virosztek, “Quantum Hellinger distances revisited,” Letters in Mathematical Physics, vol. 110, no. 8. Springer Nature, pp. 2039–2052, 2020.","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.","ista":"Pitrik J, Virosztek D. 2020. Quantum Hellinger distances revisited. Letters in Mathematical Physics. 110(8), 2039–2052."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1903.10455","open_access":"1"}],"month":"08","intvolume":" 110","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. "}],"oa_version":"Preprint","issue":"8","volume":110,"ec_funded":1,"publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"publication_status":"published","language":[{"iso":"eng"}],"article_type":"original","type":"journal_article","status":"public","_id":"7618","department":[{"_id":"LaEr"}],"date_updated":"2023-08-18T10:17:26Z"},{"department":[{"_id":"LaEr"}],"date_updated":"2023-08-24T11:16:03Z","type":"journal_article","article_type":"original","status":"public","_id":"9104","ec_funded":1,"volume":142,"publication_status":"published","publication_identifier":{"issn":["00217670"],"eissn":["15658538"]},"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1804.11199","open_access":"1"}],"scopus_import":"1","intvolume":" 142","month":"11","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"}],"oa_version":"Preprint","article_processing_charge":"No","external_id":{"isi":["000611879400008"],"arxiv":["1804.11199"]},"author":[{"first_name":"Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","last_name":"Bao","full_name":"Bao, Zhigang","orcid":"0000-0003-3036-1475"},{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Schnelli, Kevin","orcid":"0000-0003-0954-3231","last_name":"Schnelli","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin"}],"title":"On the support of the free additive convolution","citation":{"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","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","short":"Z. Bao, L. Erdös, K. Schnelli, Journal d’Analyse Mathematique 142 (2020) 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.","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.","ista":"Bao Z, Erdös L, Schnelli K. 2020. On the support of the free additive convolution. Journal d’Analyse Mathematique. 142, 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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"page":"323-348","date_created":"2021-02-07T23:01:15Z","date_published":"2020-11-01T00:00:00Z","doi":"10.1007/s11854-020-0135-2","year":"2020","isi":1,"publication":"Journal d'Analyse Mathematique","day":"01","oa":1,"quality_controlled":"1","publisher":"Springer Nature","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."},{"oa":1,"quality_controlled":"1","publisher":"Elsevier","acknowledgement":"Partially supported by ERC Advanced Grant RANMAT No. 338804.","date_created":"2022-03-18T10:18:59Z","doi":"10.1016/j.jfa.2020.108639","date_published":"2020-10-15T00:00:00Z","year":"2020","isi":1,"publication":"Journal of Functional Analysis","day":"15","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"article_number":"108639","article_processing_charge":"No","external_id":{"isi":["000559623200009"],"arxiv":["1708.01597"]},"author":[{"full_name":"Bao, Zhigang","orcid":"0000-0003-3036-1475","last_name":"Bao","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","first_name":"Zhigang"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"first_name":"Kevin","last_name":"Schnelli","full_name":"Schnelli, Kevin"}],"title":"Spectral rigidity for addition of random matrices at the regular edge","citation":{"ama":"Bao Z, Erdös L, Schnelli K. Spectral rigidity for addition of random matrices at the regular edge. Journal of Functional Analysis. 2020;279(7). doi:10.1016/j.jfa.2020.108639","apa":"Bao, Z., Erdös, L., & Schnelli, K. (2020). Spectral rigidity for addition of random matrices at the regular edge. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2020.108639","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.","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.","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.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.01597"}],"scopus_import":"1","intvolume":" 279","month":"10","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."}],"oa_version":"Preprint","ec_funded":1,"issue":"7","volume":279,"publication_status":"published","publication_identifier":{"issn":["0022-1236"]},"language":[{"iso":"eng"}],"type":"journal_article","article_type":"original","keyword":["Analysis"],"status":"public","_id":"10862","department":[{"_id":"LaEr"}],"date_updated":"2023-08-24T14:08:42Z"},{"publication_identifier":{"issn":["20103263"],"eissn":["20103271"]},"publication_status":"published","language":[{"iso":"eng"}],"issue":"3","volume":9,"ec_funded":1,"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"}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1806.08751","open_access":"1"}],"month":"07","intvolume":" 9","date_updated":"2023-08-28T08:38:48Z","department":[{"_id":"LaEr"}],"_id":"6488","type":"journal_article","article_type":"original","status":"public","isi":1,"year":"2020","day":"01","publication":"Random Matrices: Theory and Application","date_published":"2020-07-01T00:00:00Z","doi":"10.1142/S2010326320500069","date_created":"2019-05-26T21:59:14Z","quality_controlled":"1","publisher":"World Scientific Publishing","oa":1,"citation":{"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.","chicago":"Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices: Theory and Application. World Scientific Publishing, 2020. https://doi.org/10.1142/S2010326320500069.","ieee":"G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices,” Random Matrices: Theory and Application, vol. 9, no. 3. World Scientific Publishing, 2020.","short":"G. Cipolloni, L. Erdös, Random Matrices: Theory and Application 9 (2020).","ama":"Cipolloni G, Erdös L. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. 2020;9(3). doi:10.1142/S2010326320500069","apa":"Cipolloni, G., & Erdös, L. (2020). Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. World Scientific Publishing. https://doi.org/10.1142/S2010326320500069","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"}],"article_processing_charge":"No","external_id":{"arxiv":["1806.08751"],"isi":["000547464400001"]},"title":"Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices","article_number":"2050006","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program"}]},{"file_date_updated":"2020-11-18T11:14:37Z","department":[{"_id":"LaEr"}],"date_updated":"2023-09-07T12:54:12Z","ddc":["530","510"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","status":"public","_id":"6185","ec_funded":1,"license":"https://creativecommons.org/licenses/by/4.0/","related_material":{"record":[{"status":"public","id":"6179","relation":"dissertation_contains"}]},"volume":378,"publication_status":"published","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"language":[{"iso":"eng"}],"file":[{"date_updated":"2020-11-18T11:14:37Z","file_size":2904574,"creator":"dernst","date_created":"2020-11-18T11:14:37Z","file_name":"2020_CommMathPhysics_Erdoes.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"c3a683e2afdcea27afa6880b01e53dc2","file_id":"8771","success":1}],"scopus_import":"1","intvolume":" 378","month":"09","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"}],"oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000529483000001"],"arxiv":["1809.03971"]},"author":[{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"last_name":"Krüger","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"title":"Cusp universality for random matrices I: Local law and the complex Hermitian case","citation":{"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.","ista":"Erdös L, Krüger TH, Schröder DJ. 2020. Cusp universality for random matrices I: Local law and the complex Hermitian case. Communications in Mathematical Physics. 378, 1203–1278.","mla":"Erdös, László, et al. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” Communications in Mathematical Physics, vol. 378, Springer Nature, 2020, pp. 1203–78, doi:10.1007/s00220-019-03657-4.","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","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","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics 378 (2020) 1203–1278.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"page":"1203-1278","date_created":"2019-03-28T10:21:15Z","date_published":"2020-09-01T00:00:00Z","doi":"10.1007/s00220-019-03657-4","year":"2020","isi":1,"has_accepted_license":"1","publication":"Communications in Mathematical Physics","day":"01","oa":1,"publisher":"Springer Nature","quality_controlled":"1","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."}]