[{"date_created":"2020-09-11T08:35:50Z","main_file_link":[{"url":"https://arxiv.org/abs/2002.11678","open_access":"1"}],"month":"01","publication":"Linear Algebra and its Applications","publisher":"Elsevier","citation":{"short":"J. Pitrik, D. Virosztek, Linear Algebra and Its Applications 609 (2021) 203–217.","ista":"Pitrik J, Virosztek D. 2021. A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra and its Applications. 609, 203–217.","apa":"Pitrik, J., & Virosztek, D. (2021). A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. *Linear Algebra and Its Applications*. Elsevier. https://doi.org/10.1016/j.laa.2020.09.007","mla":"Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation of General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator Means.” *Linear Algebra and Its Applications*, vol. 609, Elsevier, 2021, pp. 203–17, doi:10.1016/j.laa.2020.09.007.","ama":"Pitrik J, Virosztek D. A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. *Linear Algebra and its Applications*. 2021;609:203-217. doi:10.1016/j.laa.2020.09.007","chicago":"Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation of General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator Means.” *Linear Algebra and Its Applications*. Elsevier, 2021. https://doi.org/10.1016/j.laa.2020.09.007.","ieee":"J. Pitrik and D. Virosztek, “A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means,” *Linear Algebra and its Applications*, vol. 609. Elsevier, pp. 203–217, 2021."},"department":[{"_id":"LaEr"}],"doi":"10.1016/j.laa.2020.09.007","_id":"8373","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","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"article_processing_charge":"No","oa_version":"Preprint","abstract":[{"lang":"eng","text":"It is well known that special Kubo-Ando operator means admit divergence center interpretations, moreover, they are also mean squared error estimators for certain metrics on positive definite operators. In this paper we give a divergence center interpretation for every symmetric Kubo-Ando mean. This characterization of the symmetric means naturally leads to a definition of weighted and multivariate versions of a large class of symmetric Kubo-Ando means. We study elementary properties of these weighted multivariate means, and note in particular that in the special case of the geometric mean we recover the weighted A#H-mean introduced by Kim, Lawson, and Lim."}],"keyword":["Kubo-Ando mean","weighted multivariate mean","barycenter"],"article_type":"original","author":[{"last_name":"Pitrik","full_name":"Pitrik, József","first_name":"József"},{"first_name":"Daniel","orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","last_name":"Virosztek"}],"ec_funded":1,"quality_controlled":"1","publication_identifier":{"issn":["0024-3795"]},"oa":1,"external_id":{"arxiv":["2002.11678"]},"year":"2021","intvolume":" 609","acknowledgement":"The authors are grateful to Milán Mosonyi for fruitful discussions on the topic, and to the anonymous referee for his/her comments and suggestions.\r\nJ. Pitrik was supported by the Hungarian Academy of Sciences Lendület-Momentum Grant for Quantum Information Theory, No. 96 141, and by Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K119442, no. K124152, and no. KH129601. D. Virosztek was supported by the ISTFELLOW program of the Institute of Science and Technology Austria (project code IC1027FELL01), by the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K124152, and no. KH129601.","day":"15","status":"public","publication_status":"published","type":"journal_article","date_updated":"2021-01-11T16:28:42Z","title":"A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means","volume":609,"page":"203-217","language":[{"iso":"eng"}],"date_published":"2021-01-15T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"type":"dissertation","page":"380","language":[{"iso":"eng"}],"date_published":"2021-01-25T00:00:00Z","ddc":["510"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-02-04T14:51:51Z","title":"Fluctuations in the spectrum of random matrices","year":"2021","file_date_updated":"2021-01-25T14:19:10Z","has_accepted_license":"1","publication_identifier":{"eissn":["2663-337X"]},"oa":1,"publication_status":"published","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.","day":"25","status":"public","article_processing_charge":"No","file":[{"access_level":"open_access","relation":"main_file","file_size":4127796,"content_type":"application/pdf","checksum":"5a93658a5f19478372523ee232887e2b","date_created":"2021-01-25T14:19:03Z","file_name":"thesis.pdf","creator":"gcipollo","file_id":"9043","success":1,"date_updated":"2021-01-25T14:19:03Z"},{"creator":"gcipollo","file_id":"9044","date_updated":"2021-01-25T14:19:10Z","access_level":"closed","file_size":12775206,"relation":"source_file","date_created":"2021-01-25T14:19:10Z","content_type":"application/zip","checksum":"e8270eddfe6a988e92a53c88d1d19b8c","file_name":"Thesis_files.zip"}],"oa_version":"Published Version","abstract":[{"lang":"eng","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."}],"project":[{"grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","first_name":"Giorgio"}],"ec_funded":1,"month":"01","supervisor":[{"orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2021-01-21T18:16:54Z","publisher":"IST Austria","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"alternative_title":["IST Austria Thesis"],"citation":{"ieee":"G. Cipolloni, “Fluctuations in the spectrum of random matrices,” IST Austria, 2021.","chicago":"Cipolloni, Giorgio. “Fluctuations in the Spectrum of Random Matrices.” IST Austria, 2021. https://doi.org/10.15479/AT:ISTA:9022.","mla":"Cipolloni, Giorgio. *Fluctuations in the Spectrum of Random Matrices*. IST Austria, 2021, doi:10.15479/AT:ISTA:9022.","ama":"Cipolloni G. Fluctuations in the spectrum of random matrices. 2021. doi:10.15479/AT:ISTA:9022","ista":"Cipolloni G. 2021. Fluctuations in the spectrum of random matrices. IST Austria.","short":"G. Cipolloni, Fluctuations in the Spectrum of Random Matrices, IST Austria, 2021.","apa":"Cipolloni, G. (2021). *Fluctuations in the spectrum of random matrices*. IST Austria. https://doi.org/10.15479/AT:ISTA:9022"},"doi":"10.15479/AT:ISTA:9022","_id":"9022"},{"article_processing_charge":"No","type":"preprint","oa_version":"Preprint","abstract":[{"lang":"eng","text":"We consider a model of the Riemann zeta function on the critical axis and study its maximum over intervals of length (log T)θ, where θ is either fixed or tends to zero at a suitable rate.\r\nIt is shown that the deterministic level of the maximum interpolates smoothly between the ones\r\nof log-correlated variables and of i.i.d. random variables, exhibiting a smooth transition ‘from\r\n3/4 to 1/4’ in the second order. This provides a natural context where extreme value statistics of\r\nlog-correlated variables with time-dependent variance and rate occur. A key ingredient of the\r\nproof is a precise upper tail tightness estimate for the maximum of the model on intervals of\r\nsize one, that includes a Gaussian correction. This correction is expected to be present for the\r\nRiemann zeta function and pertains to the question of the correct order of the maximum of\r\nthe zeta function in large intervals."}],"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"date_published":"2021-03-08T00:00:00Z","language":[{"iso":"eng"}],"author":[{"full_name":"Arguin, Louis-Pierre","last_name":"Arguin","first_name":"Louis-Pierre"},{"last_name":"Dubach","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","full_name":"Dubach, Guillaume","orcid":"0000-0001-6892-8137","first_name":"Guillaume"},{"first_name":"Lisa","full_name":"Hartung, Lisa","last_name":"Hartung"}],"ec_funded":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-03-09T12:07:57Z","title":"Maxima of a random model of the Riemann zeta function over intervals of varying length","external_id":{"arxiv":["2103.04817"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.04817"}],"year":"2021","month":"03","oa":1,"date_created":"2021-03-09T11:08:15Z","publication_status":"submitted","department":[{"_id":"LaEr"}],"citation":{"chicago":"Arguin, Louis-Pierre, Guillaume Dubach, and Lisa Hartung. “Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length.” *ArXiv*, n.d.","ieee":"L.-P. Arguin, G. Dubach, and L. Hartung, “Maxima of a random model of the Riemann zeta function over intervals of varying length,” *arXiv*. .","ama":"Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta function over intervals of varying length. *arXiv*.","mla":"Arguin, Louis-Pierre, et al. “Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length.” *ArXiv*, 2103.04817.","apa":"Arguin, L.-P., Dubach, G., & Hartung, L. (n.d.). Maxima of a random model of the Riemann zeta function over intervals of varying length. *arXiv*.","ista":"Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta function over intervals of varying length. arXiv, 2103.04817.","short":"L.-P. Arguin, G. Dubach, L. Hartung, ArXiv (n.d.)."},"_id":"9230","publication":"arXiv","acknowledgement":"The research of L.-P. A. is supported in part by the grant NSF CAREER DMS-1653602. G. D. gratefully acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. The research of L. H. is supported in part by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Project-ID 233630050 -TRR 146, Project-ID 443891315 within SPP 2265 and Project-ID 446173099.","article_number":"2103.04817","day":"08","status":"public"},{"publication":"arXiv","article_number":"2103.11389","status":"public","day":"21","publication_status":"draft","department":[{"_id":"LaEr"},{"_id":"ToHe"}],"citation":{"ieee":"G. Dubach and F. Mühlböck, “Formal verification of Zagier’s one-sentence proof,” *arXiv*. .","chicago":"Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence Proof.” *ArXiv*, n.d.","ama":"Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. *arXiv*.","mla":"Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence Proof.” *ArXiv*, 2103.11389.","apa":"Dubach, G., & Mühlböck, F. (n.d.). Formal verification of Zagier’s one-sentence proof. *arXiv*.","ista":"Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. arXiv, 2103.11389.","short":"G. Dubach, F. Mühlböck, ArXiv (n.d.)."},"_id":"9281","oa":1,"date_created":"2021-03-23T05:38:48Z","main_file_link":[{"url":"https://arxiv.org/abs/2103.11389","open_access":"1"}],"external_id":{"arxiv":["2103.11389"]},"year":"2021","month":"03","date_updated":"2021-03-23T09:04:32Z","title":"Formal verification of Zagier's one-sentence proof","language":[{"iso":"eng"}],"date_published":"2021-03-21T00:00:00Z","author":[{"first_name":"Guillaume","orcid":"0000-0001-6892-8137","full_name":"Dubach, Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","last_name":"Dubach"},{"first_name":"Fabian","orcid":"0000-0003-1548-0177","last_name":"Mühlböck","id":"6395C5F6-89DF-11E9-9C97-6BDFE5697425","full_name":"Mühlböck, Fabian"}],"ec_funded":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"type":"preprint","article_processing_charge":"No","oa_version":"Preprint","abstract":[{"text":"We comment on two formal proofs of Fermat's sum of two squares theorem, written using the Mathematical Components libraries of the Coq proof assistant. The first one follows Zagier's celebrated one-sentence proof; the second follows David Christopher's recent new proof relying on partition-theoretic arguments. Both formal proofs rely on a general property of involutions of finite sets, of independent interest. The proof technique consists for the most part of automating recurrent tasks (such as case distinctions and computations on natural numbers) via ad hoc tactics.","lang":"eng"}]},{"intvolume":" 380","status":"public","day":"26","article_number":"107595","acknowledgement":"D. Virosztek was supported by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K124152, and no. KH129601.","publication_status":"published","quality_controlled":"1","publication_identifier":{"issn":["0001-8708"]},"oa":1,"year":"2021","external_id":{"arxiv":["1910.10447"]},"date_updated":"2021-04-12T14:01:57Z","volume":380,"title":"The metric property of the quantum Jensen-Shannon divergence","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2021-03-26T00:00:00Z","language":[{"iso":"eng"}],"type":"journal_article","publication":"Advances in Mathematics","department":[{"_id":"LaEr"}],"citation":{"ieee":"D. Virosztek, “The metric property of the quantum Jensen-Shannon divergence,” *Advances in Mathematics*, vol. 380, no. 3. Elsevier, 2021.","chicago":"Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.” *Advances in Mathematics*. Elsevier, 2021. https://doi.org/10.1016/j.aim.2021.107595.","mla":"Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.” *Advances in Mathematics*, vol. 380, no. 3, 107595, Elsevier, 2021, doi:10.1016/j.aim.2021.107595.","ama":"Virosztek D. The metric property of the quantum Jensen-Shannon divergence. *Advances in Mathematics*. 2021;380(3). doi:10.1016/j.aim.2021.107595","ista":"Virosztek D. 2021. The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. 380(3), 107595.","short":"D. Virosztek, Advances in Mathematics 380 (2021).","apa":"Virosztek, D. (2021). The metric property of the quantum Jensen-Shannon divergence. *Advances in Mathematics*. Elsevier. https://doi.org/10.1016/j.aim.2021.107595"},"publisher":"Elsevier","_id":"9036","doi":"10.1016/j.aim.2021.107595","date_created":"2021-01-22T17:55:17Z","main_file_link":[{"url":"https://arxiv.org/abs/1910.10447","open_access":"1"}],"month":"03","keyword":["General Mathematics"],"issue":"3","ec_funded":1,"article_type":"original","author":[{"last_name":"Virosztek","full_name":"Virosztek, Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel","orcid":"0000-0003-1109-5511"}],"project":[{"grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability","call_identifier":"H2020","_id":"26A455A6-B435-11E9-9278-68D0E5697425"}],"article_processing_charge":"No","abstract":[{"text":"In this short note, we prove that the square root of the quantum Jensen-Shannon divergence is a true metric on the cone of positive matrices, and hence in particular on the quantum state space.","lang":"eng"}],"oa_version":"Preprint"},{"month":"09","date_created":"2020-10-04T22:01:37Z","_id":"8601","doi":"10.1007/s00440-020-01003-7","citation":{"chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Edge Universality for Non-Hermitian Random Matrices.” *Probability Theory and Related Fields*. Springer Nature, 2020. https://doi.org/10.1007/s00440-020-01003-7.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Edge universality for non-Hermitian random matrices,” *Probability Theory and Related Fields*. Springer Nature, 2020.","mla":"Cipolloni, Giorgio, et al. “Edge Universality for Non-Hermitian Random Matrices.” *Probability Theory and Related Fields*, Springer Nature, 2020, doi:10.1007/s00440-020-01003-7.","ama":"Cipolloni G, Erdös L, Schröder DJ. Edge universality for non-Hermitian random matrices. *Probability Theory and Related Fields*. 2020. doi:10.1007/s00440-020-01003-7","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2020).","ista":"Cipolloni G, Erdös L, Schröder DJ. 2020. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2020). Edge universality for non-Hermitian random matrices. *Probability Theory and Related Fields*. Springer Nature. https://doi.org/10.1007/s00440-020-01003-7"},"department":[{"_id":"LaEr"}],"publisher":"Springer Nature","publication":"Probability Theory and Related Fields","oa_version":"Published Version","abstract":[{"text":"We consider large non-Hermitian real or complex random matrices X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy–Widom distribution at the spectral edges of the Wigner ensemble.","lang":"eng"}],"article_processing_charge":"Yes (via OA deal)","file":[{"creator":"dernst","file_id":"8612","date_updated":"2020-10-05T14:53:40Z","success":1,"relation":"main_file","file_size":497032,"access_level":"open_access","file_name":"2020_ProbTheory_Cipolloni.pdf","date_created":"2020-10-05T14:53:40Z","content_type":"application/pdf","checksum":"611ae28d6055e1e298d53a57beb05ef4"}],"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"ec_funded":1,"author":[{"first_name":"Giorgio","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni"},{"orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"orcid":"0000-0002-2904-1856","first_name":"Dominik J","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder"}],"article_type":"original","file_date_updated":"2020-10-05T14:53:40Z","year":"2020","external_id":{"arxiv":["1908.00969"]},"oa":1,"publication_identifier":{"eissn":["14322064"],"issn":["01788051"]},"quality_controlled":"1","has_accepted_license":"1","publication_status":"published","status":"public","day":"25","type":"journal_article","scopus_import":"1","ddc":["510"],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"date_published":"2020-09-25T00:00:00Z","title":"Edge universality for non-Hermitian random matrices","date_updated":"2021-01-12T08:20:15Z"},{"project":[{"call_identifier":"H2020","_id":"26A455A6-B435-11E9-9278-68D0E5697425","name":"Geometric study of Wasserstein spaces and free probability","grant_number":"846294"}],"oa_version":"Preprint","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))."}],"article_processing_charge":"No","issue":"8","keyword":["Wasserstein space","isometric embeddings","isometric rigidity","exotic isometry flow"],"ec_funded":1,"author":[{"full_name":"Geher, Gyorgy Pal","last_name":"Geher","first_name":"Gyorgy Pal"},{"first_name":"Tamas","full_name":"Titkos, Tamas","last_name":"Titkos"},{"first_name":"Daniel","orcid":"0000-0003-1109-5511","last_name":"Virosztek","full_name":"Virosztek, Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"article_type":"original","date_created":"2020-01-29T10:20:46Z","month":"08","main_file_link":[{"url":"https://arxiv.org/abs/2002.00859","open_access":"1"}],"publication":"Transactions of the American Mathematical Society","_id":"7389","doi":"10.1090/tran/8113","citation":{"chicago":"Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Isometric Study of Wasserstein Spaces - the Real Line.” *Transactions of the American Mathematical Society*. American Mathematical Society, 2020. https://doi.org/10.1090/tran/8113.","ieee":"G. P. Geher, T. Titkos, and D. Virosztek, “Isometric study of Wasserstein spaces - the real line,” *Transactions of the American Mathematical Society*, vol. 373, no. 8. American Mathematical Society, pp. 5855–5883, 2020.","ama":"Geher GP, Titkos T, Virosztek D. Isometric study of Wasserstein spaces - the real line. *Transactions of the American Mathematical Society*. 2020;373(8):5855-5883. doi:10.1090/tran/8113","mla":"Geher, Gyorgy Pal, et al. “Isometric Study of Wasserstein Spaces - the Real Line.” *Transactions of the American Mathematical Society*, vol. 373, no. 8, American Mathematical Society, 2020, pp. 5855–83, doi:10.1090/tran/8113.","apa":"Geher, G. P., Titkos, T., & Virosztek, D. (2020). Isometric study of Wasserstein spaces - the real line. *Transactions of the American Mathematical Society*. American Mathematical Society. https://doi.org/10.1090/tran/8113","short":"G.P. Geher, T. Titkos, D. Virosztek, Transactions of the American Mathematical Society 373 (2020) 5855–5883.","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."},"department":[{"_id":"LaEr"}],"publisher":"American Mathematical Society","type":"journal_article","volume":373,"title":"Isometric study of Wasserstein spaces - the real line","date_updated":"2021-01-12T08:13:19Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ddc":["515"],"date_published":"2020-08-01T00:00:00Z","language":[{"iso":"eng"}],"page":"5855-5883","publication_identifier":{"eissn":["10886850"],"issn":["00029947"]},"oa":1,"quality_controlled":"1","year":"2020","external_id":{"arxiv":["2002.00859"]},"day":"01","status":"public","intvolume":" 373","publication_status":"published"},{"external_id":{"arxiv":["1804.11340"]},"year":"2020","quality_controlled":"1","oa":1,"publication_identifier":{"eissn":["10960783"],"issn":["00221236"]},"publication_status":"published","intvolume":" 278","article_number":"108507","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","day":"01","status":"public","type":"journal_article","scopus_import":"1","language":[{"iso":"eng"}],"date_published":"2020-07-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T08:14:00Z","title":"Local laws for polynomials of Wigner matrices","volume":278,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.11340"}],"month":"07","date_created":"2020-02-23T23:00:36Z","publisher":"Elsevier","citation":{"short":"L. Erdös, T.H. Krüger, Y. Nemish, Journal of Functional Analysis 278 (2020).","ista":"Erdös L, Krüger TH, Nemish Y. 2020. Local laws for polynomials of Wigner matrices. Journal of Functional Analysis. 278(12), 108507.","apa":"Erdös, L., Krüger, T. H., & Nemish, Y. (2020). Local laws for polynomials of Wigner matrices. *Journal of Functional Analysis*. Elsevier. https://doi.org/10.1016/j.jfa.2020.108507","ieee":"L. Erdös, T. H. Krüger, and Y. Nemish, “Local laws for polynomials of Wigner matrices,” *Journal of Functional Analysis*, vol. 278, no. 12. Elsevier, 2020.","chicago":"Erdös, László, Torben H Krüger, and Yuriy Nemish. “Local Laws for Polynomials of Wigner Matrices.” *Journal of Functional Analysis*. Elsevier, 2020. https://doi.org/10.1016/j.jfa.2020.108507.","mla":"Erdös, László, et al. “Local Laws for Polynomials of Wigner Matrices.” *Journal of Functional Analysis*, vol. 278, no. 12, 108507, Elsevier, 2020, doi:10.1016/j.jfa.2020.108507.","ama":"Erdös L, Krüger TH, Nemish Y. Local laws for polynomials of Wigner matrices. *Journal of Functional Analysis*. 2020;278(12). doi:10.1016/j.jfa.2020.108507"},"department":[{"_id":"LaEr"}],"doi":"10.1016/j.jfa.2020.108507","_id":"7512","publication":"Journal of Functional Analysis","article_processing_charge":"No","oa_version":"Preprint","abstract":[{"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.","lang":"eng"}],"project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"article_type":"original","author":[{"orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös"},{"first_name":"Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H"},{"last_name":"Nemish","full_name":"Nemish, Yuriy","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","first_name":"Yuriy","orcid":"0000-0002-7327-856X"}],"ec_funded":1,"issue":"12"},{"abstract":[{"text":"This short note aims to study quantum Hellinger distances investigated recently by Bhatia et al. (Lett Math Phys 109:1777–1804, 2019) with a particular emphasis on barycenters. We introduce the family of generalized quantum Hellinger divergences that are of the form ϕ(A,B)=Tr((1−c)A+cB−AσB), where σ is an arbitrary Kubo–Ando mean, and c∈(0,1) is the weight of σ. We note that these divergences belong to the family of maximal quantum f-divergences, and hence are jointly convex, and satisfy the data processing inequality. We derive a characterization of the barycenter of finitely many positive definite operators for these generalized quantum Hellinger divergences. We note that the characterization of the barycenter as the weighted multivariate 1/2-power mean, that was claimed in Bhatia et al. (2019), is true in the case of commuting operators, but it is not correct in the general case. ","lang":"eng"}],"oa_version":"Preprint","article_processing_charge":"No","project":[{"name":"Geometric study of Wasserstein spaces and free probability","grant_number":"846294","call_identifier":"H2020","_id":"26A455A6-B435-11E9-9278-68D0E5697425"},{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"ec_funded":1,"author":[{"first_name":"Jozsef","last_name":"Pitrik","full_name":"Pitrik, Jozsef"},{"orcid":"0000-0003-1109-5511","first_name":"Daniel","last_name":"Virosztek","full_name":"Virosztek, Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"article_type":"original","issue":"8","month":"08","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.10455"}],"date_created":"2020-03-25T15:57:48Z","_id":"7618","doi":"10.1007/s11005-020-01282-0","department":[{"_id":"LaEr"}],"citation":{"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","short":"J. Pitrik, D. Virosztek, Letters in Mathematical Physics 110 (2020) 2039–2052.","ista":"Pitrik J, Virosztek D. 2020. Quantum Hellinger distances revisited. Letters in Mathematical Physics. 110(8), 2039–2052.","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","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.","ieee":"J. Pitrik and D. Virosztek, “Quantum Hellinger distances revisited,” *Letters in Mathematical Physics*, vol. 110, no. 8. Springer Nature, pp. 2039–2052, 2020.","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."},"publisher":"Springer Nature","publication":"Letters in Mathematical Physics","type":"journal_article","scopus_import":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2020-08-01T00:00:00Z","language":[{"iso":"eng"}],"page":"2039-2052","volume":110,"title":"Quantum Hellinger distances revisited","date_updated":"2021-01-12T08:14:29Z","year":"2020","external_id":{"arxiv":["1903.10455"]},"oa":1,"publication_identifier":{"issn":["0377-9017"],"eissn":["1573-0530"]},"quality_controlled":"1","publication_status":"published","status":"public","day":"01","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"},{"ec_funded":1,"article_type":"original","author":[{"first_name":"Johannes","last_name":"Alt","full_name":"Alt, Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"Krüger, Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","last_name":"Krüger","orcid":"0000-0002-4821-3297","first_name":"Torben H"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","first_name":"Dominik J"}],"issue":"2","abstract":[{"text":"We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal edges of the self-consistent density of states. In particular, we establish a strong form of band rigidity which excludes mismatches between location and label of eigenvalues close to internal edges in these general models.","lang":"eng"}],"oa_version":"Preprint","article_processing_charge":"No","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"_id":"6184","citation":{"mla":"Alt, Johannes, et al. “Correlated Random Matrices: Band Rigidity and Edge Universality.” *Annals of Probability*, vol. 48, no. 2, Project Euclid, 2020, pp. 963–1001.","ama":"Alt J, Erdös L, Krüger TH, Schröder DJ. Correlated random matrices: Band rigidity and edge universality. *Annals of Probability*. 2020;48(2):963-1001.","chicago":"Alt, Johannes, László Erdös, Torben H Krüger, and Dominik J Schröder. “Correlated Random Matrices: Band Rigidity and Edge Universality.” *Annals of Probability*. Project Euclid, 2020.","ieee":"J. Alt, L. Erdös, T. H. Krüger, and D. J. Schröder, “Correlated random matrices: Band rigidity and edge universality,” *Annals of Probability*, vol. 48, no. 2. Project Euclid, 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.","short":"J. Alt, L. Erdös, T.H. Krüger, D.J. Schröder, Annals of Probability 48 (2020) 963–1001.","apa":"Alt, J., Erdös, L., Krüger, T. H., & Schröder, D. J. (2020). Correlated random matrices: Band rigidity and edge universality. *Annals of Probability*. Project Euclid."},"department":[{"_id":"LaEr"}],"related_material":{"record":[{"relation":"dissertation_contains","id":"6179","status":"public"},{"relation":"dissertation_contains","id":"149","status":"public"}]},"publisher":"Project Euclid","publication":"Annals of Probability","month":"03","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.07744"}],"date_created":"2019-03-28T09:20:08Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"963-1001","date_published":"2020-03-01T00:00:00Z","language":[{"iso":"eng"}],"volume":48,"title":"Correlated random matrices: Band rigidity and edge universality","date_updated":"2021-01-12T08:06:37Z","type":"journal_article","publication_status":"published","day":"01","status":"public","intvolume":" 48","year":"2020","external_id":{"arxiv":["1804.07744"]},"oa":1,"quality_controlled":"1"}]