[{"date_published":"2021-01-25T00:00:00Z","oa":1,"supervisor":[{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös"}],"citation":{"ieee":"G. Cipolloni, “Fluctuations in the spectrum of random matrices,” Institute of Science and Technology Austria, 2021.","ista":"Cipolloni G. 2021. Fluctuations in the spectrum of random matrices. Institute of Science and Technology Austria.","apa":"Cipolloni, G. (2021). <i>Fluctuations in the spectrum of random matrices</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:9022\">https://doi.org/10.15479/AT:ISTA:9022</a>","mla":"Cipolloni, Giorgio. <i>Fluctuations in the Spectrum of Random Matrices</i>. Institute of Science and Technology Austria, 2021, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:9022\">10.15479/AT:ISTA:9022</a>.","short":"G. Cipolloni, Fluctuations in the Spectrum of Random Matrices, Institute of Science and Technology Austria, 2021.","chicago":"Cipolloni, Giorgio. “Fluctuations in the Spectrum of Random Matrices.” Institute of Science and Technology Austria, 2021. <a href=\"https://doi.org/10.15479/AT:ISTA:9022\">https://doi.org/10.15479/AT:ISTA:9022</a>.","ama":"Cipolloni G. Fluctuations in the spectrum of random matrices. 2021. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:9022\">10.15479/AT:ISTA:9022</a>"},"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","doi":"10.15479/AT:ISTA:9022","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","first_name":"Giorgio"}],"date_created":"2021-01-21T18:16:54Z","_id":"9022","OA_place":"publisher","publication_identifier":{"issn":["2663-337X"]},"alternative_title":["ISTA Thesis"],"acknowledgement":"I gratefully acknowledge the financial support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385 and my advisor’s ERC Advanced Grant No. 338804.","file_date_updated":"2021-01-25T14:19:10Z","page":"380","publication_status":"published","oa_version":"Published Version","title":"Fluctuations in the spectrum of random matrices","abstract":[{"text":"In the first part of the thesis we consider Hermitian random matrices. Firstly, we consider sample covariance matrices XX∗ with X having independent identically distributed (i.i.d.) centred entries. We prove a Central Limit Theorem for differences of linear statistics of XX∗ and its minor after removing the first column of X. Secondly, we consider Wigner-type matrices and prove that the eigenvalue statistics near cusp singularities of the limiting density of states are universal and that they form a Pearcey process. Since the limiting eigenvalue distribution admits only square root (edge) and cubic root (cusp) singularities, this concludes the third and last remaining case of the Wigner-Dyson-Mehta universality conjecture. The main technical ingredients are an optimal local law at the cusp, and the proof of the fast relaxation to equilibrium of the Dyson Brownian motion in the cusp regime.\r\nIn the second part we consider non-Hermitian matrices X with centred i.i.d. entries. We normalise the entries of X to have variance N −1. It is well known that the empirical eigenvalue density converges to the uniform distribution on the unit disk (circular law). In the first project, we prove universality of the local eigenvalue statistics close to the edge of the spectrum. This is the non-Hermitian analogue of the TracyWidom universality at the Hermitian edge. Technically we analyse the evolution of the spectral distribution of X along the Ornstein-Uhlenbeck flow for very long time\r\n(up to t = +∞). In the second project, we consider linear statistics of eigenvalues for macroscopic test functions f in the Sobolev space H2+ϵ and prove their convergence to the projection of the Gaussian Free Field on the unit disk. We prove this result for non-Hermitian matrices with real or complex entries. The main technical ingredients are: (i) local law for products of two resolvents at different spectral parameters, (ii) analysis of correlated Dyson Brownian motions.\r\nIn the third and final part we discuss the mathematically rigorous application of supersymmetric techniques (SUSY ) to give a lower tail estimate of the lowest singular value of X − z, with z ∈ C. More precisely, we use superbosonisation formula to give an integral representation of the resolvent of (X − z)(X − z)∗ which reduces to two and three contour integrals in the complex and real case, respectively. The rigorous analysis of these integrals is quite challenging since simple saddle point analysis cannot be applied (the main contribution comes from a non-trivial manifold). Our result\r\nimproves classical smoothing inequalities in the regime |z| ≈ 1; this result is essential to prove edge universality for i.i.d. non-Hermitian matrices.","lang":"eng"}],"degree_awarded":"PhD","day":"25","publisher":"Institute of Science and Technology Austria","corr_author":"1","month":"01","project":[{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program","call_identifier":"H2020"},{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"type":"dissertation","year":"2021","ec_funded":1,"article_processing_charge":"No","has_accepted_license":"1","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"status":"public","file":[{"content_type":"application/pdf","date_updated":"2021-01-25T14:19:03Z","file_size":4127796,"success":1,"relation":"main_file","file_id":"9043","date_created":"2021-01-25T14:19:03Z","file_name":"thesis.pdf","checksum":"5a93658a5f19478372523ee232887e2b","creator":"gcipollo","access_level":"open_access"},{"creator":"gcipollo","access_level":"closed","file_id":"9044","date_created":"2021-01-25T14:19:10Z","file_name":"Thesis_files.zip","checksum":"e8270eddfe6a988e92a53c88d1d19b8c","relation":"source_file","file_size":12775206,"date_updated":"2021-01-25T14:19:10Z","content_type":"application/zip"}],"date_updated":"2026-04-08T06:59:33Z","ddc":["510"],"language":[{"iso":"eng"}]},{"oa_version":"Published Version","title":"The Dyson equation with linear self-energy: Spectral bands, edges and cusps","publication_status":"published","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"}],"file_date_updated":"2023-12-18T10:42:32Z","quality_controlled":"1","page":"1421-1539","article_type":"original","volume":25,"publication_identifier":{"issn":["1431-0635"],"eissn":["1431-0643"]},"intvolume":"        25","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ieee":"J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy: Spectral bands, edges and cusps,” <i>Documenta Mathematica</i>, vol. 25. EMS Press, pp. 1421–1539, 2020.","ista":"Alt J, Erdös L, Krüger TH. 2020. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. Documenta Mathematica. 25, 1421–1539.","apa":"Alt, J., Erdös, L., &#38; Krüger, T. H. (2020). The Dyson equation with linear self-energy: Spectral bands, edges and cusps. <i>Documenta Mathematica</i>. EMS Press. <a href=\"https://doi.org/10.4171/dm/780\">https://doi.org/10.4171/dm/780</a>","ama":"Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. <i>Documenta Mathematica</i>. 2020;25:1421-1539. doi:<a href=\"https://doi.org/10.4171/dm/780\">10.4171/dm/780</a>","mla":"Alt, Johannes, et al. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” <i>Documenta Mathematica</i>, vol. 25, EMS Press, 2020, pp. 1421–539, doi:<a href=\"https://doi.org/10.4171/dm/780\">10.4171/dm/780</a>.","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.” <i>Documenta Mathematica</i>. EMS Press, 2020. <a href=\"https://doi.org/10.4171/dm/780\">https://doi.org/10.4171/dm/780</a>."},"arxiv":1,"oa":1,"date_published":"2020-09-01T00:00:00Z","_id":"14694","date_created":"2023-12-18T10:37:43Z","author":[{"id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","full_name":"Alt, Johannes","last_name":"Alt","first_name":"Johannes"},{"last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"first_name":"Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger","full_name":"Krüger, Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87"}],"doi":"10.4171/dm/780","ddc":["510"],"file":[{"creator":"dernst","access_level":"open_access","checksum":"12aacc1d63b852ff9a51c1f6b218d4a6","file_name":"2020_DocumentaMathematica_Alt.pdf","file_id":"14695","date_created":"2023-12-18T10:42:32Z","relation":"main_file","success":1,"content_type":"application/pdf","file_size":1374708,"date_updated":"2023-12-18T10:42:32Z"}],"date_updated":"2025-04-15T08:05:00Z","language":[{"iso":"eng"}],"related_material":{"record":[{"status":"public","id":"6183","relation":"earlier_version"}]},"has_accepted_license":"1","department":[{"_id":"LaEr"}],"publication":"Documenta Mathematica","article_processing_charge":"Yes","status":"public","external_id":{"arxiv":["1804.07752"]},"year":"2020","type":"journal_article","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"keyword":["General Mathematics"],"license":"https://creativecommons.org/licenses/by/4.0/","day":"01","month":"09","corr_author":"1","publisher":"EMS Press"},{"quality_controlled":"1","page":"101-146","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1908.01653"}],"publication_status":"published","oa_version":"Preprint","title":"Optimal lower bound on the least singular value of the shifted Ginibre ensemble","abstract":[{"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).","lang":"eng"}],"date_published":"2020-11-16T00:00:00Z","oa":1,"citation":{"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.” <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers, 2020. <a href=\"https://doi.org/10.2140/pmp.2020.1.101\">https://doi.org/10.2140/pmp.2020.1.101</a>.","mla":"Cipolloni, Giorgio, et al. “Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble.” <i>Probability and Mathematical Physics</i>, vol. 1, no. 1, Mathematical Sciences Publishers, 2020, pp. 101–46, doi:<a href=\"https://doi.org/10.2140/pmp.2020.1.101\">10.2140/pmp.2020.1.101</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Optimal lower bound on the least singular value of the shifted Ginibre ensemble. <i>Probability and Mathematical Physics</i>. 2020;1(1):101-146. doi:<a href=\"https://doi.org/10.2140/pmp.2020.1.101\">10.2140/pmp.2020.1.101</a>","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2020). Optimal lower bound on the least singular value of the shifted Ginibre ensemble. <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/pmp.2020.1.101\">https://doi.org/10.2140/pmp.2020.1.101</a>","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.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal lower bound on the least singular value of the shifted Ginibre ensemble,” <i>Probability and Mathematical Physics</i>, vol. 1, no. 1. Mathematical Sciences Publishers, pp. 101–146, 2020."},"arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","first_name":"Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László"},{"first_name":"Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"doi":"10.2140/pmp.2020.1.101","date_created":"2024-03-04T10:27:57Z","_id":"15063","scopus_import":"1","publication_identifier":{"issn":["2690-0998"]},"volume":1,"article_type":"original","intvolume":"         1","acknowledgement":"Partially supported by ERC Advanced Grant No. 338804. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 66538","article_processing_charge":"No","publication":"Probability and Mathematical Physics","department":[{"_id":"LaEr"}],"external_id":{"arxiv":["1908.01653"]},"status":"public","date_updated":"2025-07-10T11:51:06Z","language":[{"iso":"eng"}],"day":"16","issue":"1","publisher":"Mathematical Sciences Publishers","corr_author":"1","month":"11","type":"journal_article","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","call_identifier":"H2020","name":"International IST Doctoral Program"}],"year":"2020","ec_funded":1,"keyword":["General Medicine"]},{"page":"3459-3527","status":"public","article_processing_charge":"No","publication":"Oberwolfach Reports","quality_controlled":"1","department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"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."}],"publication_status":"published","date_updated":"2024-03-12T12:25:18Z","oa_version":"None","title":"Random matrices","doi":"10.4171/owr/2019/56","date_created":"2024-03-05T07:54:44Z","author":[{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"last_name":"Götze","first_name":"Friedrich","full_name":"Götze, Friedrich"},{"last_name":"Guionnet","first_name":"Alice","full_name":"Guionnet, Alice"}],"publisher":"European Mathematical Society","_id":"15079","month":"11","date_published":"2020-11-19T00:00:00Z","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,” <i>Oberwolfach Reports</i>, vol. 16, no. 4. European Mathematical Society, pp. 3459–3527, 2020.","chicago":"Erdös, László, Friedrich Götze, and Alice Guionnet. “Random Matrices.” <i>Oberwolfach Reports</i>. European Mathematical Society, 2020. <a href=\"https://doi.org/10.4171/owr/2019/56\">https://doi.org/10.4171/owr/2019/56</a>.","mla":"Erdös, László, et al. “Random Matrices.” <i>Oberwolfach Reports</i>, vol. 16, no. 4, European Mathematical Society, 2020, pp. 3459–527, doi:<a href=\"https://doi.org/10.4171/owr/2019/56\">10.4171/owr/2019/56</a>.","short":"L. Erdös, F. Götze, A. Guionnet, Oberwolfach Reports 16 (2020) 3459–3527.","ama":"Erdös L, Götze F, Guionnet A. Random matrices. <i>Oberwolfach Reports</i>. 2020;16(4):3459-3527. doi:<a href=\"https://doi.org/10.4171/owr/2019/56\">10.4171/owr/2019/56</a>","apa":"Erdös, L., Götze, F., &#38; Guionnet, A. (2020). Random matrices. <i>Oberwolfach Reports</i>. European Mathematical Society. <a href=\"https://doi.org/10.4171/owr/2019/56\">https://doi.org/10.4171/owr/2019/56</a>"},"day":"19","issue":"4","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"        16","type":"journal_article","volume":16,"publication_identifier":{"issn":["1660-8933"]},"year":"2020","article_type":"original"},{"date_updated":"2025-04-15T08:05:01Z","language":[{"iso":"eng"}],"isi":1,"department":[{"_id":"LaEr"}],"publication":"Journal of Functional Analysis","article_processing_charge":"No","status":"public","article_number":"108639","external_id":{"isi":["000559623200009"],"arxiv":["1708.01597"]},"year":"2020","type":"journal_article","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"keyword":["Analysis"],"ec_funded":1,"issue":"7","day":"15","month":"10","corr_author":"1","publisher":"Elsevier","title":"Spectral rigidity for addition of random matrices at the regular edge","oa_version":"Preprint","publication_status":"published","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."}],"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.01597"}],"article_type":"original","volume":279,"publication_identifier":{"issn":["0022-1236"]},"acknowledgement":"Partially supported by ERC Advanced Grant RANMAT No. 338804.","intvolume":"       279","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2020). Spectral rigidity for addition of random matrices at the regular edge. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">https://doi.org/10.1016/j.jfa.2020.108639</a>","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” <i>Journal of Functional Analysis</i>. Elsevier, 2020. <a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">https://doi.org/10.1016/j.jfa.2020.108639</a>.","mla":"Bao, Zhigang, et al. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” <i>Journal of Functional Analysis</i>, vol. 279, no. 7, 108639, Elsevier, 2020, doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">10.1016/j.jfa.2020.108639</a>.","short":"Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 279 (2020).","ama":"Bao Z, Erdös L, Schnelli K. Spectral rigidity for addition of random matrices at the regular edge. <i>Journal of Functional Analysis</i>. 2020;279(7). doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">10.1016/j.jfa.2020.108639</a>","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Spectral rigidity for addition of random matrices at the regular edge,” <i>Journal of Functional Analysis</i>, vol. 279, no. 7. Elsevier, 2020.","ista":"Bao Z, Erdös L, Schnelli K. 2020. Spectral rigidity for addition of random matrices at the regular edge. Journal of Functional Analysis. 279(7), 108639."},"arxiv":1,"date_published":"2020-10-15T00:00:00Z","oa":1,"scopus_import":"1","_id":"10862","date_created":"2022-03-18T10:18:59Z","doi":"10.1016/j.jfa.2020.108639","author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","full_name":"Bao, Zhigang","orcid":"0000-0003-3036-1475","last_name":"Bao","first_name":"Zhigang"},{"orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"Schnelli, Kevin","last_name":"Schnelli","first_name":"Kevin"}]},{"page":"323-348","main_file_link":[{"url":"https://arxiv.org/abs/1804.11199","open_access":"1"}],"quality_controlled":"1","abstract":[{"lang":"eng","text":"We consider the free additive convolution of two probability measures μ and ν on the real line and show that μ ⊞ v is supported on a single interval if μ and ν each has single interval support. Moreover, the density of μ ⊞ ν is proven to vanish as a square root near the edges of its support if both μ and ν have power law behavior with exponents between −1 and 1 near their edges. In particular, these results show the ubiquity of the conditions in our recent work on optimal local law at the spectral edges for addition of random matrices [5]."}],"publication_status":"published","title":"On the support of the free additive convolution","oa_version":"Preprint","date_created":"2021-02-07T23:01:15Z","author":[{"orcid":"0000-0003-3036-1475","last_name":"Bao","first_name":"Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","full_name":"Bao, Zhigang"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László"},{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","full_name":"Schnelli, Kevin","last_name":"Schnelli","orcid":"0000-0003-0954-3231","first_name":"Kevin"}],"doi":"10.1007/s11854-020-0135-2","_id":"9104","scopus_import":"1","date_published":"2020-11-01T00:00:00Z","oa":1,"arxiv":1,"citation":{"ieee":"Z. Bao, L. Erdös, and K. Schnelli, “On the support of the free additive convolution,” <i>Journal d’Analyse Mathematique</i>, vol. 142. Springer Nature, pp. 323–348, 2020.","ista":"Bao Z, Erdös L, Schnelli K. 2020. On the support of the free additive convolution. Journal d’Analyse Mathematique. 142, 323–348.","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2020). On the support of the free additive convolution. <i>Journal d’Analyse Mathematique</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11854-020-0135-2\">https://doi.org/10.1007/s11854-020-0135-2</a>","ama":"Bao Z, Erdös L, Schnelli K. On the support of the free additive convolution. <i>Journal d’Analyse Mathematique</i>. 2020;142:323-348. doi:<a href=\"https://doi.org/10.1007/s11854-020-0135-2\">10.1007/s11854-020-0135-2</a>","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “On the Support of the Free Additive Convolution.” <i>Journal d’Analyse Mathematique</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s11854-020-0135-2\">https://doi.org/10.1007/s11854-020-0135-2</a>.","mla":"Bao, Zhigang, et al. “On the Support of the Free Additive Convolution.” <i>Journal d’Analyse Mathematique</i>, vol. 142, Springer Nature, 2020, pp. 323–48, doi:<a href=\"https://doi.org/10.1007/s11854-020-0135-2\">10.1007/s11854-020-0135-2</a>.","short":"Z. Bao, L. Erdös, K. Schnelli, Journal d’Analyse Mathematique 142 (2020) 323–348."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"       142","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.","volume":142,"publication_identifier":{"eissn":["1565-8538"],"issn":["0021-7670"]},"article_type":"original","external_id":{"isi":["000611879400008"],"arxiv":["1804.11199"]},"status":"public","article_processing_charge":"No","publication":"Journal d'Analyse Mathematique","isi":1,"department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"date_updated":"2025-07-10T12:01:37Z","publisher":"Springer Nature","month":"11","day":"01","ec_funded":1,"type":"journal_article","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"year":"2020"},{"ec_funded":1,"year":"2020","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program","call_identifier":"H2020"}],"type":"journal_article","month":"07","publisher":"World Scientific Publishing","issue":"3","day":"01","language":[{"iso":"eng"}],"date_updated":"2025-07-10T11:53:26Z","status":"public","article_number":"2050006","external_id":{"isi":["000547464400001"],"arxiv":["1806.08751"]},"isi":1,"department":[{"_id":"LaEr"}],"publication":"Random Matrices: Theory and Application","article_processing_charge":"No","intvolume":"         9","article_type":"original","publication_identifier":{"issn":["2010-3263"],"eissn":["2010-3271"]},"volume":9,"scopus_import":"1","_id":"6488","date_created":"2019-05-26T21:59:14Z","doi":"10.1142/S2010326320500069","author":[{"first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"citation":{"apa":"Cipolloni, G., &#38; Erdös, L. (2020). Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. <i>Random Matrices: Theory and Application</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S2010326320500069\">https://doi.org/10.1142/S2010326320500069</a>","chicago":"Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” <i>Random Matrices: Theory and Application</i>. World Scientific Publishing, 2020. <a href=\"https://doi.org/10.1142/S2010326320500069\">https://doi.org/10.1142/S2010326320500069</a>.","mla":"Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” <i>Random Matrices: Theory and Application</i>, vol. 9, no. 3, 2050006, World Scientific Publishing, 2020, doi:<a href=\"https://doi.org/10.1142/S2010326320500069\">10.1142/S2010326320500069</a>.","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. <i>Random Matrices: Theory and Application</i>. 2020;9(3). doi:<a href=\"https://doi.org/10.1142/S2010326320500069\">10.1142/S2010326320500069</a>","ieee":"G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices,” <i>Random Matrices: Theory and Application</i>, vol. 9, no. 3. World Scientific Publishing, 2020.","ista":"Cipolloni G, Erdös L. 2020. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. 9(3), 2050006."},"oa":1,"date_published":"2020-07-01T00:00:00Z","abstract":[{"lang":"eng","text":"We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix W˜ and its minor W. We find that the fluctuation of this difference is much smaller than those of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of W˜ and W. Our result identifies the fluctuation of the spatial derivative of the approximate Gaussian field in the recent paper by Dumitru and Paquette. Unlike in a similar result for Wigner matrices, for sample covariance matrices, the fluctuation may entirely vanish."}],"title":"Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices","oa_version":"Preprint","publication_status":"published","main_file_link":[{"url":"https://arxiv.org/abs/1806.08751","open_access":"1"}],"quality_controlled":"1"},{"day":"01","issue":"8","publisher":"American Mathematical Society","month":"08","type":"journal_article","project":[{"_id":"26A455A6-B435-11E9-9278-68D0E5697425","name":"Geometric study of Wasserstein spaces and free probability","call_identifier":"H2020","grant_number":"846294"}],"year":"2020","ec_funded":1,"keyword":["Wasserstein space","isometric embeddings","isometric rigidity","exotic isometry flow"],"article_processing_charge":"No","publication":"Transactions of the American Mathematical Society","isi":1,"department":[{"_id":"LaEr"}],"external_id":{"isi":["000551418100018"],"arxiv":["2002.00859"]},"status":"public","ddc":["515"],"date_updated":"2025-07-10T11:54:32Z","language":[{"iso":"eng"}],"oa":1,"date_published":"2020-08-01T00:00:00Z","citation":{"ieee":"G. P. Geher, T. Titkos, and D. Virosztek, “Isometric study of Wasserstein spaces - the real line,” <i>Transactions of the American Mathematical Society</i>, vol. 373, no. 8. American Mathematical Society, pp. 5855–5883, 2020.","ista":"Geher GP, Titkos T, Virosztek D. 2020. Isometric study of Wasserstein spaces - the real line. Transactions of the American Mathematical Society. 373(8), 5855–5883.","apa":"Geher, G. P., Titkos, T., &#38; Virosztek, D. (2020). Isometric study of Wasserstein spaces - the real line. <i>Transactions of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/tran/8113\">https://doi.org/10.1090/tran/8113</a>","ama":"Geher GP, Titkos T, Virosztek D. Isometric study of Wasserstein spaces - the real line. <i>Transactions of the American Mathematical Society</i>. 2020;373(8):5855-5883. doi:<a href=\"https://doi.org/10.1090/tran/8113\">10.1090/tran/8113</a>","chicago":"Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Isometric Study of Wasserstein Spaces - the Real Line.” <i>Transactions of the American Mathematical Society</i>. American Mathematical Society, 2020. <a href=\"https://doi.org/10.1090/tran/8113\">https://doi.org/10.1090/tran/8113</a>.","short":"G.P. Geher, T. Titkos, D. Virosztek, Transactions of the American Mathematical Society 373 (2020) 5855–5883.","mla":"Geher, Gyorgy Pal, et al. “Isometric Study of Wasserstein Spaces - the Real Line.” <i>Transactions of the American Mathematical Society</i>, vol. 373, no. 8, American Mathematical Society, 2020, pp. 5855–83, doi:<a href=\"https://doi.org/10.1090/tran/8113\">10.1090/tran/8113</a>."},"arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Gyorgy Pal","last_name":"Geher","full_name":"Geher, Gyorgy Pal"},{"last_name":"Titkos","first_name":"Tamas","full_name":"Titkos, Tamas"},{"first_name":"Daniel","last_name":"Virosztek","orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"doi":"10.1090/tran/8113","date_created":"2020-01-29T10:20:46Z","_id":"7389","scopus_import":"1","publication_identifier":{"issn":["0002-9947"],"eissn":["1088-6850"]},"volume":373,"article_type":"original","intvolume":"       373","quality_controlled":"1","page":"5855-5883","main_file_link":[{"url":"https://arxiv.org/abs/2002.00859","open_access":"1"}],"publication_status":"published","oa_version":"Preprint","title":"Isometric study of Wasserstein spaces - the real line","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))."}]},{"publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"volume":278,"article_type":"original","intvolume":"       278","acknowledgement":"The authors are grateful to Oskari Ajanki for his invaluable help at the initial stage of this project, to Serban Belinschi for useful discussions, to Alexander Tikhomirov for calling our attention to the model example in Section 6.2 and to the anonymous referee for suggesting to simplify certain proofs. Erdös: Partially funded by ERC Advanced Grant RANMAT No. 338804\r\n","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"date_published":"2020-07-01T00:00:00Z","arxiv":1,"citation":{"ama":"Erdös L, Krüger TH, Nemish Y. Local laws for polynomials of Wigner matrices. <i>Journal of Functional Analysis</i>. 2020;278(12). doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108507\">10.1016/j.jfa.2020.108507</a>","chicago":"Erdös, László, Torben H Krüger, and Yuriy Nemish. “Local Laws for Polynomials of Wigner Matrices.” <i>Journal of Functional Analysis</i>. Elsevier, 2020. <a href=\"https://doi.org/10.1016/j.jfa.2020.108507\">https://doi.org/10.1016/j.jfa.2020.108507</a>.","short":"L. Erdös, T.H. Krüger, Y. Nemish, Journal of Functional Analysis 278 (2020).","mla":"Erdös, László, et al. “Local Laws for Polynomials of Wigner Matrices.” <i>Journal of Functional Analysis</i>, vol. 278, no. 12, 108507, Elsevier, 2020, doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108507\">10.1016/j.jfa.2020.108507</a>.","apa":"Erdös, L., Krüger, T. H., &#38; Nemish, Y. (2020). Local laws for polynomials of Wigner matrices. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2020.108507\">https://doi.org/10.1016/j.jfa.2020.108507</a>","ista":"Erdös L, Krüger TH, Nemish Y. 2020. Local laws for polynomials of Wigner matrices. Journal of Functional Analysis. 278(12), 108507.","ieee":"L. Erdös, T. H. Krüger, and Y. Nemish, “Local laws for polynomials of Wigner matrices,” <i>Journal of Functional Analysis</i>, vol. 278, no. 12. Elsevier, 2020."},"_id":"7512","scopus_import":"1","date_created":"2020-02-23T23:00:36Z","doi":"10.1016/j.jfa.2020.108507","author":[{"first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Krüger, Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H","last_name":"Krüger","orcid":"0000-0002-4821-3297"},{"full_name":"Nemish, Yuriy","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","first_name":"Yuriy","orcid":"0000-0002-7327-856X","last_name":"Nemish"}],"title":"Local laws for polynomials of Wigner matrices","oa_version":"Preprint","publication_status":"published","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."}],"quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/1804.11340","open_access":"1"}],"year":"2020","type":"journal_article","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"ec_funded":1,"issue":"12","day":"01","month":"07","publisher":"Elsevier","date_updated":"2025-07-10T11:54:43Z","language":[{"iso":"eng"}],"publication":"Journal of Functional Analysis","department":[{"_id":"LaEr"}],"isi":1,"article_processing_charge":"No","status":"public","external_id":{"isi":["000522798900001"],"arxiv":["1804.11340"]},"article_number":"108507"},{"status":"public","external_id":{"arxiv":["1903.10455"],"isi":["000551556000002"]},"department":[{"_id":"LaEr"}],"isi":1,"publication":"Letters in Mathematical Physics","article_processing_charge":"No","language":[{"iso":"eng"}],"date_updated":"2025-10-09T08:23:15Z","month":"08","corr_author":"1","publisher":"Springer Nature","issue":"8","day":"01","ec_funded":1,"year":"2020","project":[{"name":"Geometric study of Wasserstein spaces and free probability","call_identifier":"H2020","grant_number":"846294","_id":"26A455A6-B435-11E9-9278-68D0E5697425"},{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"type":"journal_article","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.10455"}],"page":"2039-2052","quality_controlled":"1","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. "}],"title":"Quantum Hellinger distances revisited","oa_version":"Preprint","publication_status":"published","scopus_import":"1","_id":"7618","doi":"10.1007/s11005-020-01282-0","author":[{"full_name":"Pitrik, Jozsef","first_name":"Jozsef","last_name":"Pitrik"},{"full_name":"Virosztek, Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel","last_name":"Virosztek","orcid":"0000-0003-1109-5511"}],"date_created":"2020-03-25T15:57:48Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"citation":{"ieee":"J. Pitrik and D. Virosztek, “Quantum Hellinger distances revisited,” <i>Letters in Mathematical Physics</i>, vol. 110, no. 8. Springer Nature, pp. 2039–2052, 2020.","ista":"Pitrik J, Virosztek D. 2020. Quantum Hellinger distances revisited. Letters in Mathematical Physics. 110(8), 2039–2052.","apa":"Pitrik, J., &#38; Virosztek, D. (2020). Quantum Hellinger distances revisited. <i>Letters in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11005-020-01282-0\">https://doi.org/10.1007/s11005-020-01282-0</a>","ama":"Pitrik J, Virosztek D. Quantum Hellinger distances revisited. <i>Letters in Mathematical Physics</i>. 2020;110(8):2039-2052. doi:<a href=\"https://doi.org/10.1007/s11005-020-01282-0\">10.1007/s11005-020-01282-0</a>","mla":"Pitrik, Jozsef, and Daniel Virosztek. “Quantum Hellinger Distances Revisited.” <i>Letters in Mathematical Physics</i>, vol. 110, no. 8, Springer Nature, 2020, pp. 2039–52, doi:<a href=\"https://doi.org/10.1007/s11005-020-01282-0\">10.1007/s11005-020-01282-0</a>.","chicago":"Pitrik, Jozsef, and Daniel Virosztek. “Quantum Hellinger Distances Revisited.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s11005-020-01282-0\">https://doi.org/10.1007/s11005-020-01282-0</a>.","short":"J. Pitrik, D. Virosztek, Letters in Mathematical Physics 110 (2020) 2039–2052."},"date_published":"2020-08-01T00:00:00Z","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.","intvolume":"       110","article_type":"original","volume":110,"publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]}},{"article_processing_charge":"Yes (via OA deal)","publication":"Communications in Mathematical Physics","has_accepted_license":"1","department":[{"_id":"LaEr"}],"isi":1,"external_id":{"isi":["000529483000001"],"arxiv":["1809.03971"]},"status":"public","ddc":["530","510"],"file":[{"content_type":"application/pdf","date_updated":"2020-11-18T11:14:37Z","file_size":2904574,"success":1,"relation":"main_file","file_id":"8771","file_name":"2020_CommMathPhysics_Erdoes.pdf","date_created":"2020-11-18T11:14:37Z","checksum":"c3a683e2afdcea27afa6880b01e53dc2","access_level":"open_access","creator":"dernst"}],"date_updated":"2026-04-08T13:55:03Z","related_material":{"record":[{"id":"6179","status":"public","relation":"dissertation_contains"}]},"language":[{"iso":"eng"}],"day":"01","publisher":"Springer Nature","month":"09","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"type":"journal_article","year":"2020","ec_funded":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"quality_controlled":"1","file_date_updated":"2020-11-18T11:14:37Z","page":"1203-1278","publication_status":"published","title":"Cusp universality for random matrices I: Local law and the complex Hermitian case","oa_version":"Published Version","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)."}],"oa":1,"date_published":"2020-09-01T00:00:00Z","citation":{"mla":"Erdös, László, et al. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” <i>Communications in Mathematical Physics</i>, vol. 378, Springer Nature, 2020, pp. 1203–78, doi:<a href=\"https://doi.org/10.1007/s00220-019-03657-4\">10.1007/s00220-019-03657-4</a>.","chicago":"Erdös, László, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00220-019-03657-4\">https://doi.org/10.1007/s00220-019-03657-4</a>.","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics 378 (2020) 1203–1278.","ama":"Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices I: Local law and the complex Hermitian case. <i>Communications in Mathematical Physics</i>. 2020;378:1203-1278. doi:<a href=\"https://doi.org/10.1007/s00220-019-03657-4\">10.1007/s00220-019-03657-4</a>","apa":"Erdös, L., Krüger, T. H., &#38; Schröder, D. J. (2020). Cusp universality for random matrices I: Local law and the complex Hermitian case. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03657-4\">https://doi.org/10.1007/s00220-019-03657-4</a>","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.","ieee":"L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices I: Local law and the complex Hermitian case,” <i>Communications in Mathematical Physics</i>, vol. 378. Springer Nature, pp. 1203–1278, 2020."},"arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","doi":"10.1007/s00220-019-03657-4","date_created":"2019-03-28T10:21:15Z","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László"},{"full_name":"Krüger, Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger"},{"orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"_id":"6185","scopus_import":"1","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"volume":378,"article_type":"original","intvolume":"       378","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."},{"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"ieee":"J. Alt, L. Erdös, T. H. Krüger, and D. J. Schröder, “Correlated random matrices: Band rigidity and edge universality,” <i>Annals of Probability</i>, vol. 48, no. 2. Institute of Mathematical Statistics, pp. 963–1001, 2020.","ista":"Alt J, Erdös L, Krüger TH, Schröder DJ. 2020. Correlated random matrices: Band rigidity and edge universality. Annals of Probability. 48(2), 963–1001.","apa":"Alt, J., Erdös, L., Krüger, T. H., &#38; Schröder, D. J. (2020). Correlated random matrices: Band rigidity and edge universality. <i>Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/19-AOP1379\">https://doi.org/10.1214/19-AOP1379</a>","short":"J. Alt, L. Erdös, T.H. Krüger, D.J. Schröder, Annals of Probability 48 (2020) 963–1001.","chicago":"Alt, Johannes, László Erdös, Torben H Krüger, and Dominik J Schröder. “Correlated Random Matrices: Band Rigidity and Edge Universality.” <i>Annals of Probability</i>. Institute of Mathematical Statistics, 2020. <a href=\"https://doi.org/10.1214/19-AOP1379\">https://doi.org/10.1214/19-AOP1379</a>.","mla":"Alt, Johannes, et al. “Correlated Random Matrices: Band Rigidity and Edge Universality.” <i>Annals of Probability</i>, vol. 48, no. 2, Institute of Mathematical Statistics, 2020, pp. 963–1001, doi:<a href=\"https://doi.org/10.1214/19-AOP1379\">10.1214/19-AOP1379</a>.","ama":"Alt J, Erdös L, Krüger TH, Schröder DJ. Correlated random matrices: Band rigidity and edge universality. <i>Annals of Probability</i>. 2020;48(2):963-1001. doi:<a href=\"https://doi.org/10.1214/19-AOP1379\">10.1214/19-AOP1379</a>"},"arxiv":1,"date_published":"2020-03-01T00:00:00Z","oa":1,"scopus_import":"1","_id":"6184","author":[{"last_name":"Alt","first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","full_name":"Alt, Johannes"},{"first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H","last_name":"Krüger","orcid":"0000-0002-4821-3297","first_name":"Torben H"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J"}],"date_created":"2019-03-28T09:20:08Z","doi":"10.1214/19-AOP1379","article_type":"original","publication_identifier":{"issn":["0091-1798"]},"volume":48,"intvolume":"        48","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.07744"}],"page":"963-1001","oa_version":"Preprint","title":"Correlated random matrices: Band rigidity and edge universality","publication_status":"published","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."}],"day":"01","issue":"2","month":"03","publisher":"Institute of Mathematical Statistics","year":"2020","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804"}],"type":"journal_article","ec_funded":1,"isi":1,"department":[{"_id":"LaEr"}],"publication":"Annals of Probability","article_processing_charge":"No","status":"public","external_id":{"arxiv":["1804.07744"],"isi":["000528269100013"]},"date_updated":"2026-04-08T14:11:36Z","language":[{"iso":"eng"}],"related_material":{"record":[{"status":"public","id":"6179","relation":"dissertation_contains"},{"relation":"dissertation_contains","status":"public","id":"149"}]}},{"article_processing_charge":"No","department":[{"_id":"LaEr"}],"isi":1,"publication":"Journal of Spectral Theory","external_id":{"isi":["000484709400006"],"arxiv":["1701.02956"]},"status":"public","date_updated":"2024-12-11T11:49:15Z","language":[{"iso":"eng"}],"day":"01","issue":"3","publisher":"European Mathematical Society","month":"03","type":"journal_article","year":"2019","keyword":["Random Schrödinger operators","spectral shift function","Anderson orthogonality"],"quality_controlled":"1","page":"921-965","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1701.02956"}],"publication_status":"published","oa_version":"Preprint","title":"Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function","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."}],"citation":{"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.","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,” <i>Journal of Spectral Theory</i>, vol. 9, no. 3. European Mathematical Society, pp. 921–965, 2019.","mla":"Dietlein, Adrian M., et al. “Perturbations of Continuum Random Schrödinger Operators with Applications to Anderson Orthogonality and the Spectral Shift Function.” <i>Journal of Spectral Theory</i>, vol. 9, no. 3, European Mathematical Society, 2019, pp. 921–65, doi:<a href=\"https://doi.org/10.4171/jst/267\">10.4171/jst/267</a>.","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.” <i>Journal of Spectral Theory</i>. European Mathematical Society, 2019. <a href=\"https://doi.org/10.4171/jst/267\">https://doi.org/10.4171/jst/267</a>.","short":"A.M. Dietlein, M. Gebert, P. Müller, Journal of Spectral Theory 9 (2019) 921–965.","ama":"Dietlein AM, Gebert M, Müller P. Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function. <i>Journal of Spectral Theory</i>. 2019;9(3):921-965. doi:<a href=\"https://doi.org/10.4171/jst/267\">10.4171/jst/267</a>","apa":"Dietlein, A. M., Gebert, M., &#38; Müller, P. (2019). Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function. <i>Journal of Spectral Theory</i>. European Mathematical Society. <a href=\"https://doi.org/10.4171/jst/267\">https://doi.org/10.4171/jst/267</a>"},"arxiv":1,"date_published":"2019-03-01T00:00:00Z","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2022-03-18T12:36:42Z","author":[{"id":"317CB464-F248-11E8-B48F-1D18A9856A87","full_name":"Dietlein, Adrian M","last_name":"Dietlein","first_name":"Adrian M"},{"last_name":"Gebert","first_name":"Martin","full_name":"Gebert, Martin"},{"full_name":"Müller, Peter","first_name":"Peter","last_name":"Müller"}],"doi":"10.4171/jst/267","scopus_import":"1","_id":"10879","article_type":"original","volume":9,"publication_identifier":{"issn":["1664-039X"]},"acknowledgement":"M.G. was supported by the DFG under grant GE 2871/1-1.","intvolume":"         9"},{"publication":"Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics","department":[{"_id":"LaEr"}],"article_processing_charge":"No","status":"public","external_id":{"arxiv":["1902.08750"]},"article_number":"34","date_updated":"2021-01-12T08:17:18Z","language":[{"iso":"eng"}],"day":"01","month":"07","conference":{"location":"Ljubljana, Slovenia","name":"FPSAC: International Conference on Formal Power Series and Algebraic Combinatorics","start_date":"2019-07-01","end_date":"2019-07-05"},"publisher":"Formal Power Series and Algebraic Combinatorics","year":"2019","type":"conference","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804"},{"grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"ec_funded":1,"quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/1902.08750","open_access":"1"}],"title":"New edge asymptotics of skew Young diagrams via free boundaries","oa_version":"Preprint","publication_status":"published","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."}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2019-07-01T00:00:00Z","oa":1,"citation":{"apa":"Betea, D., Bouttier, J., Nejjar, P., &#38; Vuletíc, M. (2019). New edge asymptotics of skew Young diagrams via free boundaries. In <i>Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics</i>. Ljubljana, Slovenia: Formal Power Series and Algebraic Combinatorics.","mla":"Betea, Dan, et al. “New Edge Asymptotics of Skew Young Diagrams via Free Boundaries.” <i>Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics</i>, 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 <i>Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics</i>. Formal Power Series and Algebraic Combinatorics, 2019.","ama":"Betea D, Bouttier J, Nejjar P, Vuletíc M. New edge asymptotics of skew Young diagrams via free boundaries. In: <i>Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics</i>. Formal Power Series and Algebraic Combinatorics; 2019.","ieee":"D. Betea, J. Bouttier, P. Nejjar, and M. Vuletíc, “New edge asymptotics of skew Young diagrams via free boundaries,” in <i>Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics</i>, Ljubljana, Slovenia, 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."},"arxiv":1,"_id":"8175","scopus_import":"1","date_created":"2020-07-26T22:01:04Z","author":[{"full_name":"Betea, Dan","last_name":"Betea","first_name":"Dan"},{"full_name":"Bouttier, Jérémie","last_name":"Bouttier","first_name":"Jérémie"},{"first_name":"Peter","last_name":"Nejjar","full_name":"Nejjar, Peter","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Mirjana","last_name":"Vuletíc","full_name":"Vuletíc, Mirjana"}],"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"},{"language":[{"iso":"eng"}],"date_updated":"2025-04-15T06:50:24Z","status":"public","external_id":{"isi":["000459725600012"],"arxiv":["1601.06118"]},"department":[{"_id":"LaEr"}],"isi":1,"publication":"Ergodic Theory and Dynamical Systems","article_processing_charge":"No","ec_funded":1,"year":"2019","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"type":"journal_article","month":"04","publisher":"Cambridge University Press","day":"01","issue":"4","abstract":[{"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.","lang":"eng"}],"oa_version":"Preprint","title":"Singular analytic linear cocycles with negative infinite Lyapunov exponents","publication_status":"published","main_file_link":[{"url":"https://arxiv.org/abs/1601.06118","open_access":"1"}],"page":"1082-1098","quality_controlled":"1","intvolume":"        39","volume":39,"scopus_import":"1","_id":"6086","doi":"10.1017/etds.2017.52","author":[{"first_name":"Christian","orcid":"0000-0001-8255-3968","last_name":"Sadel","full_name":"Sadel, Christian","id":"4760E9F8-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Xu, Disheng","first_name":"Disheng","last_name":"Xu"}],"date_created":"2019-03-10T22:59:18Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","arxiv":1,"citation":{"ama":"Sadel C, Xu D. Singular analytic linear cocycles with negative infinite Lyapunov exponents. <i>Ergodic Theory and Dynamical Systems</i>. 2019;39(4):1082-1098. doi:<a href=\"https://doi.org/10.1017/etds.2017.52\">10.1017/etds.2017.52</a>","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.” <i>Ergodic Theory and Dynamical Systems</i>, vol. 39, no. 4, Cambridge University Press, 2019, pp. 1082–98, doi:<a href=\"https://doi.org/10.1017/etds.2017.52\">10.1017/etds.2017.52</a>.","chicago":"Sadel, Christian, and Disheng Xu. “Singular Analytic Linear Cocycles with Negative Infinite Lyapunov Exponents.” <i>Ergodic Theory and Dynamical Systems</i>. Cambridge University Press, 2019. <a href=\"https://doi.org/10.1017/etds.2017.52\">https://doi.org/10.1017/etds.2017.52</a>.","apa":"Sadel, C., &#38; Xu, D. (2019). Singular analytic linear cocycles with negative infinite Lyapunov exponents. <i>Ergodic Theory and Dynamical Systems</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/etds.2017.52\">https://doi.org/10.1017/etds.2017.52</a>","ista":"Sadel C, Xu D. 2019. Singular analytic linear cocycles with negative infinite Lyapunov exponents. Ergodic Theory and Dynamical Systems. 39(4), 1082–1098.","ieee":"C. Sadel and D. Xu, “Singular analytic linear cocycles with negative infinite Lyapunov exponents,” <i>Ergodic Theory and Dynamical Systems</i>, vol. 39, no. 4. Cambridge University Press, pp. 1082–1098, 2019."},"date_published":"2019-04-01T00:00:00Z","oa":1},{"publication_status":"published","oa_version":"Preprint","title":"Local single ring theorem on optimal scale","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"}],"quality_controlled":"1","page":"1270-1334","main_file_link":[{"url":"https://arxiv.org/abs/1612.05920","open_access":"1"}],"publication_identifier":{"issn":["0091-1798"]},"volume":47,"intvolume":"        47","date_published":"2019-05-01T00:00:00Z","oa":1,"citation":{"chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Single Ring Theorem on Optimal Scale.” <i>Annals of Probability</i>. Institute of Mathematical Statistics, 2019. <a href=\"https://doi.org/10.1214/18-AOP1284\">https://doi.org/10.1214/18-AOP1284</a>.","mla":"Bao, Zhigang, et al. “Local Single Ring Theorem on Optimal Scale.” <i>Annals of Probability</i>, vol. 47, no. 3, Institute of Mathematical Statistics, 2019, pp. 1270–334, doi:<a href=\"https://doi.org/10.1214/18-AOP1284\">10.1214/18-AOP1284</a>.","short":"Z. Bao, L. Erdös, K. Schnelli, Annals of Probability 47 (2019) 1270–1334.","ama":"Bao Z, Erdös L, Schnelli K. Local single ring theorem on optimal scale. <i>Annals of Probability</i>. 2019;47(3):1270-1334. doi:<a href=\"https://doi.org/10.1214/18-AOP1284\">10.1214/18-AOP1284</a>","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2019). Local single ring theorem on optimal scale. <i>Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/18-AOP1284\">https://doi.org/10.1214/18-AOP1284</a>","ista":"Bao Z, Erdös L, Schnelli K. 2019. Local single ring theorem on optimal scale. Annals of Probability. 47(3), 1270–1334.","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Local single ring theorem on optimal scale,” <i>Annals of Probability</i>, vol. 47, no. 3. Institute of Mathematical Statistics, pp. 1270–1334, 2019."},"arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2019-06-02T21:59:13Z","doi":"10.1214/18-AOP1284","author":[{"first_name":"Zhigang","orcid":"0000-0003-3036-1475","last_name":"Bao","full_name":"Bao, Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603"},{"first_name":"Kevin","orcid":"0000-0003-0954-3231","last_name":"Schnelli","full_name":"Schnelli, Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87"}],"_id":"6511","scopus_import":"1","date_updated":"2025-07-10T11:53:28Z","language":[{"iso":"eng"}],"article_processing_charge":"No","publication":"Annals of Probability","department":[{"_id":"LaEr"}],"isi":1,"external_id":{"isi":["000466616100003"],"arxiv":["1612.05920"]},"status":"public","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"type":"journal_article","year":"2019","ec_funded":1,"day":"01","issue":"3","publisher":"Institute of Mathematical Statistics","month":"05"},{"article_processing_charge":"No","publication":"Journal of Mathematical Analysis and Applications","isi":1,"department":[{"_id":"LaEr"}],"external_id":{"isi":["000486563900031"],"arxiv":["1809.01101"]},"article_number":"123435","status":"public","date_updated":"2025-07-10T11:53:55Z","language":[{"iso":"eng"}],"day":"15","issue":"2","publisher":"Elsevier","month":"12","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"type":"journal_article","year":"2019","ec_funded":1,"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1809.01101"}],"publication_status":"published","oa_version":"Preprint","title":"On isometric embeddings of Wasserstein spaces – the discrete case","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<p<∞ is any parameter value. Roughly speaking, we will prove that any isometric embedding can be described by a special kind of X×(0,1]-indexed family of nonnegative finite measures. Our result implies that a typical non-surjective isometric embedding of Wp(X) splits mass and does not preserve the shape of measures. In order to stress that the lack of surjectivity is what makes things challenging, we will prove alternatively that Wp(X) is isometrically rigid for all 0<p<∞.","lang":"eng"}],"oa":1,"date_published":"2019-12-15T00:00:00Z","arxiv":1,"citation":{"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.","ieee":"G. P. Gehér, T. Titkos, and D. Virosztek, “On isometric embeddings of Wasserstein spaces – the discrete case,” <i>Journal of Mathematical Analysis and Applications</i>, vol. 480, no. 2. Elsevier, 2019.","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.” <i>Journal of Mathematical Analysis and Applications</i>, vol. 480, no. 2, 123435, Elsevier, 2019, doi:<a href=\"https://doi.org/10.1016/j.jmaa.2019.123435\">10.1016/j.jmaa.2019.123435</a>.","chicago":"Gehér, György Pál, Tamás Titkos, and Daniel Virosztek. “On Isometric Embeddings of Wasserstein Spaces – the Discrete Case.” <i>Journal of Mathematical Analysis and Applications</i>. Elsevier, 2019. <a href=\"https://doi.org/10.1016/j.jmaa.2019.123435\">https://doi.org/10.1016/j.jmaa.2019.123435</a>.","ama":"Gehér GP, Titkos T, Virosztek D. On isometric embeddings of Wasserstein spaces – the discrete case. <i>Journal of Mathematical Analysis and Applications</i>. 2019;480(2). doi:<a href=\"https://doi.org/10.1016/j.jmaa.2019.123435\">10.1016/j.jmaa.2019.123435</a>","apa":"Gehér, G. P., Titkos, T., &#38; Virosztek, D. (2019). On isometric embeddings of Wasserstein spaces – the discrete case. <i>Journal of Mathematical Analysis and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jmaa.2019.123435\">https://doi.org/10.1016/j.jmaa.2019.123435</a>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Gehér, György Pál","first_name":"György Pál","last_name":"Gehér"},{"full_name":"Titkos, Tamás","last_name":"Titkos","first_name":"Tamás"},{"orcid":"0000-0003-1109-5511","last_name":"Virosztek","first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","full_name":"Virosztek, Daniel"}],"doi":"10.1016/j.jmaa.2019.123435","date_created":"2019-09-01T22:01:01Z","_id":"6843","scopus_import":"1","publication_identifier":{"eissn":["1096-0813"],"issn":["0022-247X"]},"volume":480,"article_type":"original","intvolume":"       480"},{"language":[{"iso":"eng"}],"date_updated":"2025-06-30T09:55:30Z","status":"public","department":[{"_id":"LaEr"}],"publication":"Kyoto RIMS Kôkyûroku","article_processing_charge":"No","ec_funded":1,"year":"2019","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"type":"conference","month":"01","corr_author":"1","publisher":"Research Institute for Mathematical Sciences, Kyoto University","conference":{"end_date":"2019-01-30","name":"Research on isometries as preserver problems and related topics","start_date":"2019-01-28","location":"Kyoto, Japan"},"OA_type":"green","day":"30","abstract":[{"lang":"eng","text":"The aim of this short note is to expound one particular issue that was discussed during the talk [10] given at the symposium ”Researches on isometries as preserver problems and related topics” at Kyoto RIMS. That is,  the role of Dirac masses by  describing  the  isometry group of various metric spaces  of probability  measures.   This  article  is  of  survey  character,  and  it  does  not  contain  any  essentially  new results.From an isometric point of view, in some cases, metric spaces of measures are similar to C(K)-type function  spaces.   Similarity  means  here  that  their  isometries  are  driven  by  some  nice  transformations of  the  underlying  space.   Of  course,  it  depends  on  the  particular  choice  of  the  metric  how  nice  these transformations should be.  Sometimes, as we will see, being a homeomorphism is enough to generate an isometry.  But sometimes we need more:  the transformation must preserve the underlying distance as well.  Statements claiming that isometries in questions are necessarily induced by homeomorphisms are called Banach-Stone-type results, while results asserting that the underlying transformation is necessarily an isometry are termed as isometric rigidity results.As  Dirac  masses  can  be  considered  as  building  bricks  of  the  set  of  all  Borel  measures,  a  natural question arises:Is it enough to understand how an isometry acts on the set of Dirac masses?  Does this action extend uniquely to all measures?In what follows, we will thoroughly investigate this question."}],"oa_version":"Submitted Version","title":"Dirac masses and isometric rigidity","publication_status":"published","main_file_link":[{"open_access":"1","url":"http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/2125.html"}],"page":"34-41","quality_controlled":"1","acknowledgement":"This paper is part of a long term collaboration investigating the isometric structure of Wasserstein\r\nspaces. The authors would like to thank the warm hospitality and generosity of László Erdós and his\r\ngroup at Institute of Science and Technology Austria.\r\nT. Titkos wants to thank Oriental Business and Innovation Center ‐ OBIC for providing financial\r\nsupport to participate in the symposium at the Kyoto RIMS.\r\nGy. P. Gehér was supported by the Leverhulme Trust Early Career Fellowship (ECF‐2018‐125),\r\nand also by the Hungarian National Research, Development and Innovation Office (K115383). T.\r\nTitkos was supported by the Hungarian National Research, Development and Innovation Office‐ NKFIH\r\n(PD128374), by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the\r\nUNKP‐18‐4‐BGE‐3 New National Excellence Program of the Ministry of Human Capacities. D. Virosztek\r\nwas supported by the ISTFELLOW program of the Institute of Science and Technology Austria (project\r\ncode IC1027FELL01 ) and partially supported by the Hungarian National Research, Development and\r\nInnovation Office NKFIH (grant no. K124152 and grant no. KH129601)","intvolume":"      2125","volume":2125,"OA_place":"repository","_id":"7035","author":[{"full_name":"Geher, Gyorgy Pal","first_name":"Gyorgy Pal","last_name":"Geher"},{"last_name":"Titkos","first_name":"Tamas","full_name":"Titkos, Tamas"},{"id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","full_name":"Virosztek, Daniel","orcid":"0000-0003-1109-5511","last_name":"Virosztek","first_name":"Daniel"}],"date_created":"2019-11-18T15:39:53Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ama":"Geher GP, Titkos T, Virosztek D. Dirac masses and isometric rigidity. In: <i>Kyoto RIMS Kôkyûroku</i>. Vol 2125. Research Institute for Mathematical Sciences, Kyoto University; 2019:34-41.","chicago":"Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Dirac Masses and Isometric Rigidity.” In <i>Kyoto RIMS Kôkyûroku</i>, 2125:34–41. Research Institute for Mathematical Sciences, Kyoto University, 2019.","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.” <i>Kyoto RIMS Kôkyûroku</i>, vol. 2125, Research Institute for Mathematical Sciences, Kyoto University, 2019, pp. 34–41.","apa":"Geher, G. P., Titkos, T., &#38; Virosztek, D. (2019). Dirac masses and isometric rigidity. In <i>Kyoto RIMS Kôkyûroku</i> (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.","ieee":"G. P. Geher, T. Titkos, and D. Virosztek, “Dirac masses and isometric rigidity,” in <i>Kyoto RIMS Kôkyûroku</i>, Kyoto, Japan, 2019, vol. 2125, pp. 34–41."},"date_published":"2019-01-30T00:00:00Z","oa":1},{"issue":"3","day":"25","month":"09","publisher":"Institute of Mathematical Statistics","year":"2019","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"}],"type":"journal_article","ec_funded":1,"isi":1,"department":[{"_id":"LaEr"},{"_id":"JaMa"}],"publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","article_processing_charge":"No","status":"public","external_id":{"arxiv":["1710.02323"],"isi":["000487763200001"]},"date_updated":"2025-04-14T07:27:49Z","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"citation":{"ieee":"P. Ferrari, P. Ghosal, and P. Nejjar, “Limit law of a second class particle in TASEP with non-random initial condition,” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol. 55, no. 3. Institute of Mathematical Statistics, pp. 1203–1225, 2019.","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.","apa":"Ferrari, P., Ghosal, P., &#38; Nejjar, P. (2019). Limit law of a second class particle in TASEP with non-random initial condition. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/18-AIHP916\">https://doi.org/10.1214/18-AIHP916</a>","chicago":"Ferrari, Patrick, Promit Ghosal, and Peter Nejjar. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics, 2019. <a href=\"https://doi.org/10.1214/18-AIHP916\">https://doi.org/10.1214/18-AIHP916</a>.","mla":"Ferrari, Patrick, et al. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol. 55, no. 3, Institute of Mathematical Statistics, 2019, pp. 1203–25, doi:<a href=\"https://doi.org/10.1214/18-AIHP916\">10.1214/18-AIHP916</a>.","short":"P. Ferrari, P. Ghosal, P. Nejjar, Annales de l’institut Henri Poincare (B) Probability and Statistics 55 (2019) 1203–1225.","ama":"Ferrari P, Ghosal P, Nejjar P. Limit law of a second class particle in TASEP with non-random initial condition. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. 2019;55(3):1203-1225. doi:<a href=\"https://doi.org/10.1214/18-AIHP916\">10.1214/18-AIHP916</a>"},"date_published":"2019-09-25T00:00:00Z","oa":1,"scopus_import":"1","_id":"72","author":[{"last_name":"Ferrari","first_name":"Patrick","full_name":"Ferrari, Patrick"},{"full_name":"Ghosal, Promit","last_name":"Ghosal","first_name":"Promit"},{"last_name":"Nejjar","first_name":"Peter","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","full_name":"Nejjar, Peter"}],"doi":"10.1214/18-AIHP916","date_created":"2018-12-11T11:44:29Z","article_type":"original","publication_identifier":{"issn":["0246-0203"]},"volume":55,"intvolume":"        55","quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1710.02323"}],"page":"1203-1225","oa_version":"Preprint","title":"Limit law of a second class particle in TASEP with non-random initial condition","publication_status":"published","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&lt;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."}]},{"year":"2019","type":"journal_article","day":"01","issue":"1","month":"02","publisher":"Institute of Mathematical Statistics","date_updated":"2023-09-06T14:58:39Z","language":[{"iso":"eng"}],"publication":"Annales de l'Institut Henri Poincaré, Probabilités et Statistiques","department":[{"_id":"LaEr"}],"isi":1,"article_processing_charge":"No","status":"public","external_id":{"isi":["000456070200013"],"arxiv":["1704.05224"]},"publication_identifier":{"issn":["0246-0203"]},"volume":55,"article_type":"original","intvolume":"        55","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa":1,"date_published":"2019-02-01T00:00:00Z","arxiv":1,"citation":{"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. <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>. 2019;55(1):441-479. doi:<a href=\"https://doi.org/10.1214/18-aihp888\">10.1214/18-aihp888</a>","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.” <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>, vol. 55, no. 1, Institute of Mathematical Statistics, 2019, pp. 441–79, doi:<a href=\"https://doi.org/10.1214/18-aihp888\">10.1214/18-aihp888</a>.","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.” <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>. Institute of Mathematical Statistics, 2019. <a href=\"https://doi.org/10.1214/18-aihp888\">https://doi.org/10.1214/18-aihp888</a>.","apa":"Akemann, G., Checinski, T., Liu, D., &#38; Strahov, E. (2019). Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles. <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/18-aihp888\">https://doi.org/10.1214/18-aihp888</a>","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.","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,” <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>, vol. 55, no. 1. Institute of Mathematical Statistics, pp. 441–479, 2019."},"_id":"7423","date_created":"2020-01-30T10:36:50Z","doi":"10.1214/18-aihp888","author":[{"last_name":"Akemann","first_name":"Gernot","full_name":"Akemann, Gernot"},{"full_name":"Checinski, Tomasz","last_name":"Checinski","first_name":"Tomasz"},{"id":"2F947E34-F248-11E8-B48F-1D18A9856A87","full_name":"Liu, Dangzheng","last_name":"Liu","first_name":"Dangzheng"},{"full_name":"Strahov, Eugene","last_name":"Strahov","first_name":"Eugene"}],"title":"Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles","oa_version":"Preprint","publication_status":"published","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"}],"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1704.05224"}],"page":"441-479"}]