[{"publication_identifier":{"issn":["0001-8708"]},"month":"03","doi":"10.1016/j.aim.2021.107595","language":[{"iso":"eng"}],"external_id":{"arxiv":["1910.10447"],"isi":["000619676100035"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.10447"}],"oa":1,"project":[{"_id":"26A455A6-B435-11E9-9278-68D0E5697425","grant_number":"846294","call_identifier":"H2020","name":"Geometric study of Wasserstein spaces and free probability"}],"isi":1,"quality_controlled":"1","ec_funded":1,"article_number":"107595","author":[{"last_name":"Virosztek","first_name":"Daniel","orcid":"0000-0003-1109-5511","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","full_name":"Virosztek, Daniel"}],"volume":380,"date_created":"2021-01-22T17:55:17Z","date_updated":"2023-08-07T13:34:48Z","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.","year":"2021","publisher":"Elsevier","department":[{"_id":"LaEr"}],"publication_status":"published","article_processing_charge":"No","day":"26","keyword":["General Mathematics"],"date_published":"2021-03-26T00:00:00Z","citation":{"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.","short":"D. Virosztek, Advances in Mathematics 380 (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.","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.","ieee":"D. Virosztek, “The metric property of the quantum Jensen-Shannon divergence,” Advances in Mathematics, vol. 380, no. 3. Elsevier, 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"},"publication":"Advances in Mathematics","article_type":"original","issue":"3","abstract":[{"lang":"eng","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."}],"type":"journal_article","oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"9036","intvolume":" 380","title":"The metric property of the quantum Jensen-Shannon divergence","status":"public"},{"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"},{"first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"date_updated":"2023-08-08T13:39:19Z","date_created":"2021-05-23T22:01:44Z","volume":26,"year":"2021","publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","file_date_updated":"2021-05-25T13:24:19Z","ec_funded":1,"license":"https://creativecommons.org/licenses/by/4.0/","article_number":"24","doi":"10.1214/21-EJP591","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["2002.02438"],"isi":["000641855600001"]},"oa":1,"quality_controlled":"1","isi":1,"project":[{"grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","name":"International IST Doctoral Program","call_identifier":"H2020"}],"month":"03","publication_identifier":{"eissn":["10836489"]},"oa_version":"Published Version","file":[{"relation":"main_file","file_id":"9423","checksum":"864ab003ad4cffea783f65aa8c2ba69f","success":1,"date_created":"2021-05-25T13:24:19Z","date_updated":"2021-05-25T13:24:19Z","access_level":"open_access","file_name":"2021_EJP_Cipolloni.pdf","content_type":"application/pdf","file_size":865148,"creator":"kschuh"}],"_id":"9412","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","ddc":["510"],"title":"Fluctuation around the circular law for random matrices with real entries","intvolume":" 26","abstract":[{"lang":"eng","text":"We extend our recent result [22] on the central limit theorem for the linear eigenvalue statistics of non-Hermitian matrices X with independent, identically distributed complex entries to the real symmetry class. We find that the expectation and variance substantially differ from their complex counterparts, reflecting (i) the special spectral symmetry of real matrices onto the real axis; and (ii) the fact that real i.i.d. matrices have many real eigenvalues. Our result generalizes the previously known special cases where either the test function is analytic [49] or the first four moments of the matrix elements match the real Gaussian [59, 44]. The key element of the proof is the analysis of several weakly dependent Dyson Brownian motions (DBMs). The conceptual novelty of the real case compared with [22] is that the correlation structure of the stochastic differentials in each individual DBM is non-trivial, potentially even jeopardising its well-posedness."}],"type":"journal_article","date_published":"2021-03-23T00:00:00Z","publication":"Electronic Journal of Probability","citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. Fluctuation around the circular law for random matrices with real entries. Electronic Journal of Probability. 2021;26. doi:10.1214/21-EJP591","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Fluctuation around the circular law for random matrices with real entries,” Electronic Journal of Probability, vol. 26. Institute of Mathematical Statistics, 2021.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Fluctuation around the circular law for random matrices with real entries. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-EJP591","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Fluctuation around the circular law for random matrices with real entries. Electronic Journal of Probability. 26, 24.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 26 (2021).","mla":"Cipolloni, Giorgio, et al. “Fluctuation around the Circular Law for Random Matrices with Real Entries.” Electronic Journal of Probability, vol. 26, 24, Institute of Mathematical Statistics, 2021, doi:10.1214/21-EJP591.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Fluctuation around the Circular Law for Random Matrices with Real Entries.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2021. https://doi.org/10.1214/21-EJP591."},"day":"23","article_processing_charge":"No","has_accepted_license":"1","scopus_import":"1"},{"abstract":[{"lang":"eng","text":"We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principle for quantum systems whose components are modelled by Wigner matrices. "}],"type":"journal_article","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"9555","checksum":"47c986578de132200d41e6d391905519","success":1,"date_updated":"2021-06-15T14:40:45Z","date_created":"2021-06-15T14:40:45Z","access_level":"open_access","file_name":"2021_ForumMath_Bao.pdf","content_type":"application/pdf","file_size":483458,"creator":"cziletti"}],"intvolume":" 9","status":"public","ddc":["510"],"title":"Equipartition principle for Wigner matrices","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"9550","has_accepted_license":"1","article_processing_charge":"No","day":"27","scopus_import":"1","date_published":"2021-05-27T00:00:00Z","article_type":"original","citation":{"chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Equipartition Principle for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge University Press, 2021. https://doi.org/10.1017/fms.2021.38.","short":"Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021).","mla":"Bao, Zhigang, et al. “Equipartition Principle for Wigner Matrices.” Forum of Mathematics, Sigma, vol. 9, e44, Cambridge University Press, 2021, doi:10.1017/fms.2021.38.","apa":"Bao, Z., Erdös, L., & Schnelli, K. (2021). Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2021.38","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,” Forum of Mathematics, Sigma, vol. 9. Cambridge University Press, 2021.","ista":"Bao Z, Erdös L, Schnelli K. 2021. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 9, e44.","ama":"Bao Z, Erdös L, Schnelli K. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 2021;9. doi:10.1017/fms.2021.38"},"publication":"Forum of Mathematics, Sigma","ec_funded":1,"file_date_updated":"2021-06-15T14:40:45Z","article_number":"e44","volume":9,"date_updated":"2023-08-08T14:03:40Z","date_created":"2021-06-13T22:01:33Z","author":[{"last_name":"Bao","first_name":"Zhigang","orcid":"0000-0003-3036-1475","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","full_name":"Bao, Zhigang"},{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"Schnelli, Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0954-3231","first_name":"Kevin","last_name":"Schnelli"}],"department":[{"_id":"LaEr"}],"publisher":"Cambridge University Press","publication_status":"published","year":"2021","acknowledgement":"The first author is supported in part by Hong Kong RGC Grant GRF 16301519 and NSFC 11871425. The second author is supported in part by ERC Advanced Grant RANMAT 338804. The third author is supported in part by Swedish Research Council Grant VR-2017-05195 and the Knut and Alice Wallenberg Foundation","publication_identifier":{"eissn":["20505094"]},"month":"05","language":[{"iso":"eng"}],"doi":"10.1017/fms.2021.38","project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"}],"quality_controlled":"1","isi":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"isi":["000654960800001"],"arxiv":["2008.07061"]}},{"acknowledgement":"The authors are very grateful to Yan Fyodorov for discussions on the physical background and for providing references, and to the anonymous referee for numerous valuable remarks.","year":"2021","publisher":"Springer Nature","department":[{"_id":"LaEr"}],"publication_status":"published","author":[{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","last_name":"Krüger","first_name":"Torben H","full_name":"Krüger, Torben H"},{"full_name":"Nemish, Yuriy","orcid":"0000-0002-7327-856X","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","last_name":"Nemish","first_name":"Yuriy"}],"volume":22,"date_created":"2021-08-15T22:01:29Z","date_updated":"2023-08-11T10:31:48Z","ec_funded":1,"file_date_updated":"2022-05-12T12:50:27Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"oa":1,"external_id":{"arxiv":["1911.05112"],"isi":["000681531500001"]},"project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"}],"quality_controlled":"1","isi":1,"doi":"10.1007/s00023-021-01085-6","language":[{"iso":"eng"}],"publication_identifier":{"issn":["1424-0637"],"eissn":["1424-0661"]},"month":"12","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"9912","intvolume":" 22","title":"Scattering in quantum dots via noncommutative rational functions","status":"public","ddc":["510"],"oa_version":"Published Version","file":[{"checksum":"8d6bac0e2b0a28539608b0538a8e3b38","success":1,"date_updated":"2022-05-12T12:50:27Z","date_created":"2022-05-12T12:50:27Z","relation":"main_file","file_id":"11365","content_type":"application/pdf","file_size":1162454,"creator":"dernst","access_level":"open_access","file_name":"2021_AnnHenriPoincare_Erdoes.pdf"}],"type":"journal_article","abstract":[{"lang":"eng","text":"In the customary random matrix model for transport in quantum dots with M internal degrees of freedom coupled to a chaotic environment via 𝑁≪𝑀 channels, the density 𝜌 of transmission eigenvalues is computed from a specific invariant ensemble for which explicit formula for the joint probability density of all eigenvalues is available. We revisit this problem in the large N regime allowing for (i) arbitrary ratio 𝜙:=𝑁/𝑀≤1; and (ii) general distributions for the matrix elements of the Hamiltonian of the quantum dot. In the limit 𝜙→0, we recover the formula for the density 𝜌 that Beenakker (Rev Mod Phys 69:731–808, 1997) has derived for a special matrix ensemble. We also prove that the inverse square root singularity of the density at zero and full transmission in Beenakker’s formula persists for any 𝜙<1 but in the borderline case 𝜙=1 an anomalous 𝜆−2/3 singularity arises at zero. To access this level of generality, we develop the theory of global and local laws on the spectral density of a large class of noncommutative rational expressions in large random matrices with i.i.d. entries."}],"citation":{"chicago":"Erdös, László, Torben H Krüger, and Yuriy Nemish. “Scattering in Quantum Dots via Noncommutative Rational Functions.” Annales Henri Poincaré . Springer Nature, 2021. https://doi.org/10.1007/s00023-021-01085-6.","mla":"Erdös, László, et al. “Scattering in Quantum Dots via Noncommutative Rational Functions.” Annales Henri Poincaré , vol. 22, Springer Nature, 2021, pp. 4205–4269, doi:10.1007/s00023-021-01085-6.","short":"L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré 22 (2021) 4205–4269.","ista":"Erdös L, Krüger TH, Nemish Y. 2021. Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . 22, 4205–4269.","ieee":"L. Erdös, T. H. Krüger, and Y. Nemish, “Scattering in quantum dots via noncommutative rational functions,” Annales Henri Poincaré , vol. 22. Springer Nature, pp. 4205–4269, 2021.","apa":"Erdös, L., Krüger, T. H., & Nemish, Y. (2021). Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . Springer Nature. https://doi.org/10.1007/s00023-021-01085-6","ama":"Erdös L, Krüger TH, Nemish Y. Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . 2021;22:4205–4269. doi:10.1007/s00023-021-01085-6"},"publication":"Annales Henri Poincaré ","page":"4205–4269","article_type":"original","date_published":"2021-12-01T00:00:00Z","scopus_import":"1","has_accepted_license":"1","article_processing_charge":"Yes (in subscription journal)","day":"01"},{"type":"journal_article","issue":"2","abstract":[{"lang":"eng","text":"We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension. Our theorem thus rigorously verifies the Eigenstate Thermalisation Hypothesis by Deutsch (Phys Rev A 43:2046–2049, 1991) for the simplest chaotic quantum system, the Wigner ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity (QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing previous probabilistic QUE results in Bourgade and Yau (Commun Math Phys 350:231–278, 2017) and Bourgade et al. (Commun Pure Appl Math 73:1526–1596, 2020)."}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"10221","intvolume":" 388","title":"Eigenstate thermalization hypothesis for Wigner matrices","status":"public","ddc":["510"],"file":[{"success":1,"checksum":"a2c7b6f5d23b5453cd70d1261272283b","date_created":"2022-02-02T10:19:55Z","date_updated":"2022-02-02T10:19:55Z","file_id":"10715","relation":"main_file","creator":"cchlebak","file_size":841426,"content_type":"application/pdf","access_level":"open_access","file_name":"2021_CommunMathPhys_Cipolloni.pdf"}],"oa_version":"Published Version","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"29","citation":{"chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” Communications in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s00220-021-04239-z.","mla":"Cipolloni, Giorgio, et al. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” Communications in Mathematical Physics, vol. 388, no. 2, Springer Nature, 2021, pp. 1005–1048, doi:10.1007/s00220-021-04239-z.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 388 (2021) 1005–1048.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 388(2), 1005–1048.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Eigenstate thermalization hypothesis for Wigner matrices,” Communications in Mathematical Physics, vol. 388, no. 2. Springer Nature, pp. 1005–1048, 2021.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-021-04239-z","ama":"Cipolloni G, Erdös L, Schröder DJ. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 2021;388(2):1005–1048. doi:10.1007/s00220-021-04239-z"},"publication":"Communications in Mathematical Physics","page":"1005–1048","article_type":"original","date_published":"2021-10-29T00:00:00Z","file_date_updated":"2022-02-02T10:19:55Z","year":"2021","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","publisher":"Springer Nature","department":[{"_id":"LaEr"}],"publication_status":"published","author":[{"orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","first_name":"Giorgio","full_name":"Cipolloni, Giorgio"},{"full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","first_name":"Dominik J"}],"volume":388,"date_updated":"2023-08-14T10:29:49Z","date_created":"2021-11-07T23:01:25Z","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"month":"10","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"arxiv":["2012.13215"],"isi":["000712232700001"]},"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"quality_controlled":"1","isi":1,"doi":"10.1007/s00220-021-04239-z","language":[{"iso":"eng"}]},{"oa":1,"project":[{"call_identifier":"H2020","name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"},{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"}],"doi":"10.15479/AT:ISTA:9022","degree_awarded":"PhD","supervisor":[{"full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"}],"language":[{"iso":"eng"}],"month":"01","publication_identifier":{"issn":["2663-337X"]},"year":"2021","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.","publication_status":"published","publisher":"Institute of Science and Technology Austria","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"author":[{"last_name":"Cipolloni","first_name":"Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"}],"date_created":"2021-01-21T18:16:54Z","date_updated":"2023-09-07T13:29:32Z","file_date_updated":"2021-01-25T14:19:10Z","ec_funded":1,"citation":{"short":"G. Cipolloni, Fluctuations in the Spectrum of Random Matrices, Institute of Science and Technology Austria, 2021.","mla":"Cipolloni, Giorgio. Fluctuations in the Spectrum of Random Matrices. Institute of Science and Technology Austria, 2021, doi:10.15479/AT:ISTA:9022.","chicago":"Cipolloni, Giorgio. “Fluctuations in the Spectrum of Random Matrices.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/AT:ISTA:9022.","ama":"Cipolloni G. Fluctuations in the spectrum of random matrices. 2021. doi:10.15479/AT:ISTA:9022","ieee":"G. Cipolloni, “Fluctuations in the spectrum of random matrices,” Institute of Science and Technology Austria, 2021.","apa":"Cipolloni, G. (2021). Fluctuations in the spectrum of random matrices. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:9022","ista":"Cipolloni G. 2021. Fluctuations in the spectrum of random matrices. Institute of Science and Technology Austria."},"page":"380","date_published":"2021-01-25T00:00:00Z","day":"25","has_accepted_license":"1","article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"9022","status":"public","ddc":["510"],"title":"Fluctuations in the spectrum of random matrices","oa_version":"Published Version","file":[{"file_size":4127796,"content_type":"application/pdf","creator":"gcipollo","file_name":"thesis.pdf","access_level":"open_access","date_created":"2021-01-25T14:19:03Z","date_updated":"2021-01-25T14:19:03Z","checksum":"5a93658a5f19478372523ee232887e2b","success":1,"relation":"main_file","file_id":"9043"},{"file_size":12775206,"content_type":"application/zip","creator":"gcipollo","access_level":"closed","file_name":"Thesis_files.zip","checksum":"e8270eddfe6a988e92a53c88d1d19b8c","date_updated":"2021-01-25T14:19:10Z","date_created":"2021-01-25T14:19:10Z","relation":"source_file","file_id":"9044"}],"type":"dissertation","alternative_title":["ISTA Thesis"],"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."}]},{"ec_funded":1,"publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Mathematical Sciences Publishers","year":"2021","acknowledgement":"Partially supported by ERC Starting Grant RandMat No. 715539 and the SwissMap grant of Swiss National Science Foundation. Partially supported by ERC Advanced Grant RanMat No. 338804. Partially supported by the Hausdorff Center for Mathematics in Bonn.","date_created":"2024-02-18T23:01:03Z","date_updated":"2024-02-19T08:30:00Z","volume":2,"author":[{"first_name":"Johannes","last_name":"Alt","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","full_name":"Alt, Johannes"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"last_name":"Krüger","first_name":"Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H"}],"month":"05","publication_identifier":{"issn":["2690-0998"],"eissn":["2690-1005"]},"quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"external_id":{"arxiv":["1907.13631"]},"oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1907.13631","open_access":"1"}],"language":[{"iso":"eng"}],"doi":"10.2140/pmp.2021.2.221","type":"journal_article","abstract":[{"text":"We consider random n×n matrices X with independent and centered entries and a general variance profile. We show that the spectral radius of X converges with very high probability to the square root of the spectral radius of the variance matrix of X when n tends to infinity. We also establish the optimal rate of convergence, that is a new result even for general i.i.d. matrices beyond the explicitly solvable Gaussian cases. The main ingredient is the proof of the local inhomogeneous circular law [arXiv:1612.07776] at the spectral edge.","lang":"eng"}],"issue":"2","title":"Spectral radius of random matrices with independent entries","status":"public","intvolume":" 2","_id":"15013","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","scopus_import":"1","day":"21","article_processing_charge":"No","article_type":"original","page":"221-280","publication":"Probability and Mathematical Physics","citation":{"ieee":"J. Alt, L. Erdös, and T. H. Krüger, “Spectral radius of random matrices with independent entries,” Probability and Mathematical Physics, vol. 2, no. 2. Mathematical Sciences Publishers, pp. 221–280, 2021.","apa":"Alt, J., Erdös, L., & Krüger, T. H. (2021). Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. Mathematical Sciences Publishers. https://doi.org/10.2140/pmp.2021.2.221","ista":"Alt J, Erdös L, Krüger TH. 2021. Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. 2(2), 221–280.","ama":"Alt J, Erdös L, Krüger TH. Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. 2021;2(2):221-280. doi:10.2140/pmp.2021.2.221","chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “Spectral Radius of Random Matrices with Independent Entries.” Probability and Mathematical Physics. Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/pmp.2021.2.221.","short":"J. Alt, L. Erdös, T.H. Krüger, Probability and Mathematical Physics 2 (2021) 221–280.","mla":"Alt, Johannes, et al. “Spectral Radius of Random Matrices with Independent Entries.” Probability and Mathematical Physics, vol. 2, no. 2, Mathematical Sciences Publishers, 2021, pp. 221–80, doi:10.2140/pmp.2021.2.221."},"date_published":"2021-05-21T00:00:00Z"},{"scopus_import":"1","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"01","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2021).","mla":"Cipolloni, Giorgio, et al. “Edge Universality for Non-Hermitian Random Matrices.” Probability Theory and Related Fields, Springer Nature, 2021, doi:10.1007/s00440-020-01003-7.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Edge Universality for Non-Hermitian Random Matrices.” Probability Theory and Related Fields. Springer Nature, 2021. https://doi.org/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. 2021. doi:10.1007/s00440-020-01003-7","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields. Springer Nature. 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, 2021.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields."},"publication":"Probability Theory and Related Fields","article_type":"original","date_published":"2021-02-01T00:00:00Z","type":"journal_article","abstract":[{"lang":"eng","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."}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"8601","status":"public","title":"Edge universality for non-Hermitian random matrices","ddc":["510"],"oa_version":"Published Version","file":[{"relation":"main_file","file_id":"8612","date_created":"2020-10-05T14:53:40Z","date_updated":"2020-10-05T14:53:40Z","checksum":"611ae28d6055e1e298d53a57beb05ef4","success":1,"file_name":"2020_ProbTheory_Cipolloni.pdf","access_level":"open_access","file_size":497032,"content_type":"application/pdf","creator":"dernst"}],"publication_identifier":{"issn":["01788051"],"eissn":["14322064"]},"month":"02","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000572724600002"],"arxiv":["1908.00969"]},"oa":1,"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program","call_identifier":"H2020"}],"quality_controlled":"1","isi":1,"doi":"10.1007/s00440-020-01003-7","language":[{"iso":"eng"}],"ec_funded":1,"file_date_updated":"2020-10-05T14:53:40Z","year":"2021","department":[{"_id":"LaEr"}],"publisher":"Springer Nature","publication_status":"published","author":[{"full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","first_name":"Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","first_name":"Dominik J","full_name":"Schröder, Dominik J"}],"date_created":"2020-10-04T22:01:37Z","date_updated":"2024-03-07T15:07:53Z"},{"citation":{"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","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.","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","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.","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.” Transactions of the American Mathematical Society, vol. 373, no. 8, American Mathematical Society, 2020, pp. 5855–83, doi:10.1090/tran/8113.","chicago":"Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Isometric Study of Wasserstein Spaces - the Real Line.” Transactions of the American Mathematical Society. American Mathematical Society, 2020. https://doi.org/10.1090/tran/8113."},"publication":"Transactions of the American Mathematical Society","page":"5855-5883","article_type":"original","date_published":"2020-08-01T00:00:00Z","keyword":["Wasserstein space","isometric embeddings","isometric rigidity","exotic isometry flow"],"article_processing_charge":"No","day":"01","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"7389","intvolume":" 373","status":"public","title":"Isometric study of Wasserstein spaces - the real line","ddc":["515"],"oa_version":"Preprint","type":"journal_article","issue":"8","abstract":[{"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)).","lang":"eng"}],"oa":1,"external_id":{"arxiv":["2002.00859"],"isi":["000551418100018"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2002.00859"}],"project":[{"grant_number":"846294","_id":"26A455A6-B435-11E9-9278-68D0E5697425","name":"Geometric study of Wasserstein spaces and free probability","call_identifier":"H2020"}],"isi":1,"quality_controlled":"1","doi":"10.1090/tran/8113","language":[{"iso":"eng"}],"publication_identifier":{"issn":["00029947"],"eissn":["10886850"]},"month":"08","year":"2020","publisher":"American Mathematical Society","department":[{"_id":"LaEr"}],"publication_status":"published","author":[{"last_name":"Geher","first_name":"Gyorgy Pal","full_name":"Geher, Gyorgy Pal"},{"first_name":"Tamas","last_name":"Titkos","full_name":"Titkos, Tamas"},{"last_name":"Virosztek","first_name":"Daniel","orcid":"0000-0003-1109-5511","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","full_name":"Virosztek, Daniel"}],"volume":373,"date_created":"2020-01-29T10:20:46Z","date_updated":"2023-08-17T14:31:03Z","ec_funded":1},{"month":"07","publication_identifier":{"eissn":["10960783"],"issn":["00221236"]},"external_id":{"isi":["000522798900001"],"arxiv":["1804.11340"]},"main_file_link":[{"url":"https://arxiv.org/abs/1804.11340","open_access":"1"}],"oa":1,"isi":1,"quality_controlled":"1","project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"}],"doi":"10.1016/j.jfa.2020.108507","language":[{"iso":"eng"}],"article_number":"108507","ec_funded":1,"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","year":"2020","publication_status":"published","publisher":"Elsevier","department":[{"_id":"LaEr"}],"author":[{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"Krüger, Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","first_name":"Torben H","last_name":"Krüger"},{"full_name":"Nemish, Yuriy","last_name":"Nemish","first_name":"Yuriy","orcid":"0000-0002-7327-856X","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87"}],"date_created":"2020-02-23T23:00:36Z","date_updated":"2023-08-18T06:36:10Z","volume":278,"scopus_import":"1","day":"01","article_processing_charge":"No","publication":"Journal of Functional Analysis","citation":{"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.","ista":"Erdös L, Krüger TH, Nemish Y. 2020. Local laws for polynomials of Wigner matrices. Journal of Functional Analysis. 278(12), 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","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.","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.” Journal of Functional Analysis, vol. 278, no. 12, 108507, Elsevier, 2020, doi:10.1016/j.jfa.2020.108507."},"article_type":"original","date_published":"2020-07-01T00:00:00Z","type":"journal_article","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"}],"issue":"12","_id":"7512","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"Local laws for polynomials of Wigner matrices","status":"public","intvolume":" 278","oa_version":"Preprint"}]