[{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.10447"}],"external_id":{"arxiv":["1910.10447"],"isi":["000619676100035"]},"oa":1,"isi":1,"quality_controlled":"1","project":[{"grant_number":"846294","_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Geometric study of Wasserstein spaces and free probability"}],"doi":"10.1016/j.aim.2021.107595","language":[{"iso":"eng"}],"month":"03","publication_identifier":{"issn":["0001-8708"]},"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","publication_status":"published","publisher":"Elsevier","department":[{"_id":"LaEr"}],"author":[{"full_name":"Virosztek, Daniel","first_name":"Daniel","last_name":"Virosztek","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-1109-5511"}],"date_created":"2021-01-22T17:55:17Z","date_updated":"2023-08-07T13:34:48Z","volume":380,"article_number":"107595","ec_funded":1,"publication":"Advances in Mathematics","citation":{"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.","short":"D. Virosztek, Advances in Mathematics 380 (2021).","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","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"},"article_type":"original","date_published":"2021-03-26T00:00:00Z","keyword":["General Mathematics"],"day":"26","article_processing_charge":"No","_id":"9036","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","title":"The metric property of the quantum Jensen-Shannon divergence","intvolume":" 380","oa_version":"Preprint","type":"journal_article","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"}],"issue":"3"},{"file_date_updated":"2021-05-25T13:24:19Z","ec_funded":1,"license":"https://creativecommons.org/licenses/by/4.0/","article_number":"24","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","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856"}],"date_created":"2021-05-23T22:01:44Z","date_updated":"2023-08-08T13:39:19Z","volume":26,"year":"2021","publication_status":"published","publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"month":"03","publication_identifier":{"eissn":["10836489"]},"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":{"isi":["000641855600001"],"arxiv":["2002.02438"]},"oa":1,"quality_controlled":"1","isi":1,"project":[{"name":"International IST Doctoral Program","call_identifier":"H2020","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"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","oa_version":"Published Version","file":[{"file_id":"9423","relation":"main_file","success":1,"checksum":"864ab003ad4cffea783f65aa8c2ba69f","date_created":"2021-05-25T13:24:19Z","date_updated":"2021-05-25T13:24:19Z","access_level":"open_access","file_name":"2021_EJP_Cipolloni.pdf","creator":"kschuh","file_size":865148,"content_type":"application/pdf"}],"_id":"9412","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","ddc":["510"],"title":"Fluctuation around the circular law for random matrices with real entries","status":"public","intvolume":" 26","day":"23","article_processing_charge":"No","has_accepted_license":"1","scopus_import":"1","date_published":"2021-03-23T00:00:00Z","publication":"Electronic Journal of Probability","citation":{"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.","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","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","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.","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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 26 (2021)."}},{"date_published":"2021-05-27T00:00:00Z","article_type":"original","citation":{"ama":"Bao Z, Erdös L, Schnelli K. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 2021;9. 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.","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.","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."},"publication":"Forum of Mathematics, Sigma","has_accepted_license":"1","article_processing_charge":"No","day":"27","scopus_import":"1","file":[{"checksum":"47c986578de132200d41e6d391905519","success":1,"date_updated":"2021-06-15T14:40:45Z","date_created":"2021-06-15T14:40:45Z","relation":"main_file","file_id":"9555","content_type":"application/pdf","file_size":483458,"creator":"cziletti","access_level":"open_access","file_name":"2021_ForumMath_Bao.pdf"}],"oa_version":"Published Version","intvolume":" 9","status":"public","ddc":["510"],"title":"Equipartition principle for Wigner matrices","_id":"9550","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","abstract":[{"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. ","lang":"eng"}],"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1017/fms.2021.38","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"isi":1,"quality_controlled":"1","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":{"isi":["000654960800001"],"arxiv":["2008.07061"]},"publication_identifier":{"eissn":["20505094"]},"month":"05","volume":9,"date_updated":"2023-08-08T14:03:40Z","date_created":"2021-06-13T22:01:33Z","author":[{"orcid":"0000-0003-3036-1475","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","last_name":"Bao","first_name":"Zhigang","full_name":"Bao, Zhigang"},{"full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"full_name":"Schnelli, Kevin","last_name":"Schnelli","first_name":"Kevin","orcid":"0000-0003-0954-3231","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87"}],"department":[{"_id":"LaEr"}],"publisher":"Cambridge University Press","publication_status":"published","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","year":"2021","ec_funded":1,"file_date_updated":"2021-06-15T14:40:45Z","article_number":"e44"},{"abstract":[{"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.","lang":"eng"}],"type":"journal_article","oa_version":"Published Version","file":[{"date_updated":"2022-05-12T12:50:27Z","date_created":"2022-05-12T12:50:27Z","success":1,"checksum":"8d6bac0e2b0a28539608b0538a8e3b38","file_id":"11365","relation":"main_file","creator":"dernst","content_type":"application/pdf","file_size":1162454,"file_name":"2021_AnnHenriPoincare_Erdoes.pdf","access_level":"open_access"}],"intvolume":" 22","status":"public","title":"Scattering in quantum dots via noncommutative rational functions","ddc":["510"],"_id":"9912","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","has_accepted_license":"1","article_processing_charge":"Yes (in subscription journal)","day":"01","scopus_import":"1","date_published":"2021-12-01T00:00:00Z","page":"4205–4269","article_type":"original","citation":{"ista":"Erdös L, Krüger TH, Nemish Y. 2021. Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . 22, 4205–4269.","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","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.","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","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."},"publication":"Annales Henri Poincaré ","ec_funded":1,"file_date_updated":"2022-05-12T12:50:27Z","volume":22,"date_updated":"2023-08-11T10:31:48Z","date_created":"2021-08-15T22:01:29Z","author":[{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"},{"last_name":"Krüger","first_name":"Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H"},{"last_name":"Nemish","first_name":"Yuriy","orcid":"0000-0002-7327-856X","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","full_name":"Nemish, Yuriy"}],"department":[{"_id":"LaEr"}],"publisher":"Springer Nature","publication_status":"published","year":"2021","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.","publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]},"month":"12","language":[{"iso":"eng"}],"doi":"10.1007/s00023-021-01085-6","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"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":["000681531500001"],"arxiv":["1911.05112"]}},{"has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","day":"29","scopus_import":"1","date_published":"2021-10-29T00:00:00Z","citation":{"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","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","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.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 388(2), 1005–1048.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 388 (2021) 1005–1048.","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.","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."},"publication":"Communications in Mathematical Physics","page":"1005–1048","article_type":"original","issue":"2","abstract":[{"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).","lang":"eng"}],"type":"journal_article","oa_version":"Published Version","file":[{"content_type":"application/pdf","file_size":841426,"creator":"cchlebak","access_level":"open_access","file_name":"2021_CommunMathPhys_Cipolloni.pdf","checksum":"a2c7b6f5d23b5453cd70d1261272283b","success":1,"date_created":"2022-02-02T10:19:55Z","date_updated":"2022-02-02T10:19:55Z","relation":"main_file","file_id":"10715"}],"_id":"10221","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 388","title":"Eigenstate thermalization hypothesis for Wigner matrices","status":"public","ddc":["510"],"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"month":"10","doi":"10.1007/s00220-021-04239-z","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":{"isi":["000712232700001"],"arxiv":["2012.13215"]},"oa":1,"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"isi":1,"quality_controlled":"1","file_date_updated":"2022-02-02T10:19:55Z","author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","first_name":"Giorgio","last_name":"Cipolloni"},{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Schröder","first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"volume":388,"date_updated":"2023-08-14T10:29:49Z","date_created":"2021-11-07T23:01:25Z","year":"2021","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","department":[{"_id":"LaEr"}],"publisher":"Springer Nature","publication_status":"published"},{"date_updated":"2023-09-07T13:29:32Z","date_created":"2021-01-21T18:16:54Z","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio"}],"publication_status":"published","publisher":"Institute of Science and Technology Austria","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"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.","year":"2021","file_date_updated":"2021-01-25T14:19:10Z","ec_funded":1,"degree_awarded":"PhD","supervisor":[{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"}],"language":[{"iso":"eng"}],"doi":"10.15479/AT:ISTA:9022","project":[{"grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"International IST Doctoral Program"},{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"oa":1,"month":"01","publication_identifier":{"issn":["2663-337X"]},"file":[{"access_level":"open_access","file_name":"thesis.pdf","creator":"gcipollo","file_size":4127796,"content_type":"application/pdf","file_id":"9043","relation":"main_file","success":1,"checksum":"5a93658a5f19478372523ee232887e2b","date_created":"2021-01-25T14:19:03Z","date_updated":"2021-01-25T14:19:03Z"},{"file_id":"9044","relation":"source_file","checksum":"e8270eddfe6a988e92a53c88d1d19b8c","date_updated":"2021-01-25T14:19:10Z","date_created":"2021-01-25T14:19:10Z","access_level":"closed","file_name":"Thesis_files.zip","creator":"gcipollo","content_type":"application/zip","file_size":12775206}],"oa_version":"Published Version","title":"Fluctuations in the spectrum of random matrices","ddc":["510"],"status":"public","_id":"9022","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","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"}],"alternative_title":["ISTA Thesis"],"type":"dissertation","date_published":"2021-01-25T00:00:00Z","page":"380","citation":{"mla":"Cipolloni, Giorgio. Fluctuations in the Spectrum of Random Matrices. Institute of Science and Technology Austria, 2021, doi:10.15479/AT:ISTA:9022.","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. 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","ista":"Cipolloni G. 2021. Fluctuations in the spectrum of random matrices. Institute of Science and Technology Austria.","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","ieee":"G. Cipolloni, “Fluctuations in the spectrum of random matrices,” Institute of Science and Technology Austria, 2021."},"day":"25","has_accepted_license":"1","article_processing_charge":"No"},{"external_id":{"arxiv":["1907.13631"]},"oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1907.13631","open_access":"1"}],"quality_controlled":"1","project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"doi":"10.2140/pmp.2021.2.221","language":[{"iso":"eng"}],"month":"05","publication_identifier":{"issn":["2690-0998"],"eissn":["2690-1005"]},"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.","publication_status":"published","publisher":"Mathematical Sciences Publishers","department":[{"_id":"LaEr"}],"author":[{"full_name":"Alt, Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","last_name":"Alt","first_name":"Johannes"},{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Krüger, Torben H","last_name":"Krüger","first_name":"Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2024-02-19T08:30:00Z","date_created":"2024-02-18T23:01:03Z","volume":2,"ec_funded":1,"publication":"Probability and Mathematical Physics","citation":{"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","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","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.","ista":"Alt J, Erdös L, Krüger TH. 2021. Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. 2(2), 221–280.","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.","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."},"article_type":"original","page":"221-280","date_published":"2021-05-21T00:00:00Z","scopus_import":"1","day":"21","article_processing_charge":"No","_id":"15013","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","title":"Spectral radius of random matrices with independent entries","intvolume":" 2","oa_version":"Preprint","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"},{"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"}],"type":"journal_article","oa_version":"Published Version","file":[{"file_size":497032,"content_type":"application/pdf","creator":"dernst","file_name":"2020_ProbTheory_Cipolloni.pdf","access_level":"open_access","date_created":"2020-10-05T14:53:40Z","date_updated":"2020-10-05T14:53:40Z","checksum":"611ae28d6055e1e298d53a57beb05ef4","success":1,"relation":"main_file","file_id":"8612"}],"_id":"8601","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","status":"public","ddc":["510"],"title":"Edge universality for non-Hermitian random matrices","day":"01","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)","scopus_import":"1","date_published":"2021-02-01T00:00:00Z","publication":"Probability Theory and Related Fields","citation":{"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.","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."},"article_type":"original","file_date_updated":"2020-10-05T14:53:40Z","ec_funded":1,"author":[{"last_name":"Cipolloni","first_name":"Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"full_name":"Schröder, Dominik J","last_name":"Schröder","first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2024-03-07T15:07:53Z","date_created":"2020-10-04T22:01:37Z","year":"2021","publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Springer Nature","month":"02","publication_identifier":{"eissn":["14322064"],"issn":["01788051"]},"doi":"10.1007/s00440-020-01003-7","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":{"isi":["000572724600002"],"arxiv":["1908.00969"]},"oa":1,"isi":1,"quality_controlled":"1","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","call_identifier":"H2020","name":"International IST Doctoral Program"}]},{"intvolume":" 373","status":"public","ddc":["515"],"title":"Isometric study of Wasserstein spaces - the real line","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"7389","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"}],"page":"5855-5883","article_type":"original","citation":{"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.","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","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.","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."},"publication":"Transactions of the American Mathematical Society","date_published":"2020-08-01T00:00:00Z","keyword":["Wasserstein space","isometric embeddings","isometric rigidity","exotic isometry flow"],"article_processing_charge":"No","day":"01","department":[{"_id":"LaEr"}],"publisher":"American Mathematical Society","publication_status":"published","year":"2020","volume":373,"date_updated":"2023-08-17T14:31:03Z","date_created":"2020-01-29T10:20:46Z","author":[{"first_name":"Gyorgy Pal","last_name":"Geher","full_name":"Geher, Gyorgy Pal"},{"last_name":"Titkos","first_name":"Tamas","full_name":"Titkos, Tamas"},{"full_name":"Virosztek, Daniel","first_name":"Daniel","last_name":"Virosztek","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-1109-5511"}],"ec_funded":1,"project":[{"_id":"26A455A6-B435-11E9-9278-68D0E5697425","grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability","call_identifier":"H2020"}],"isi":1,"quality_controlled":"1","external_id":{"isi":["000551418100018"],"arxiv":["2002.00859"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/2002.00859","open_access":"1"}],"language":[{"iso":"eng"}],"doi":"10.1090/tran/8113","publication_identifier":{"eissn":["10886850"],"issn":["00029947"]},"month":"08"},{"type":"journal_article","issue":"12","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."}],"_id":"7512","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 278","status":"public","title":"Local laws for polynomials of Wigner matrices","oa_version":"Preprint","scopus_import":"1","article_processing_charge":"No","day":"01","citation":{"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.","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.","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.","short":"L. Erdös, T.H. Krüger, Y. Nemish, Journal of Functional Analysis 278 (2020)."},"publication":"Journal of Functional Analysis","article_type":"original","date_published":"2020-07-01T00:00:00Z","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","publisher":"Elsevier","department":[{"_id":"LaEr"}],"publication_status":"published","author":[{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","last_name":"Krüger","first_name":"Torben H"},{"orcid":"0000-0002-7327-856X","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","last_name":"Nemish","first_name":"Yuriy","full_name":"Nemish, Yuriy"}],"volume":278,"date_updated":"2023-08-18T06:36:10Z","date_created":"2020-02-23T23:00:36Z","publication_identifier":{"eissn":["10960783"],"issn":["00221236"]},"month":"07","main_file_link":[{"url":"https://arxiv.org/abs/1804.11340","open_access":"1"}],"external_id":{"isi":["000522798900001"],"arxiv":["1804.11340"]},"oa":1,"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"isi":1,"quality_controlled":"1","doi":"10.1016/j.jfa.2020.108507","language":[{"iso":"eng"}]},{"scopus_import":"1","day":"01","article_processing_charge":"No","publication":"Letters in Mathematical Physics","citation":{"short":"J. Pitrik, D. Virosztek, Letters in Mathematical Physics 110 (2020) 2039–2052.","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.","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.","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","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","ieee":"J. Pitrik and D. Virosztek, “Quantum Hellinger distances revisited,” Letters in Mathematical Physics, 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."},"article_type":"original","page":"2039-2052","date_published":"2020-08-01T00:00:00Z","type":"journal_article","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"}],"issue":"8","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"7618","title":"Quantum Hellinger distances revisited","status":"public","intvolume":" 110","oa_version":"Preprint","month":"08","publication_identifier":{"issn":["0377-9017"],"eissn":["1573-0530"]},"main_file_link":[{"url":"https://arxiv.org/abs/1903.10455","open_access":"1"}],"external_id":{"arxiv":["1903.10455"],"isi":["000551556000002"]},"oa":1,"quality_controlled":"1","isi":1,"project":[{"_id":"26A455A6-B435-11E9-9278-68D0E5697425","grant_number":"846294","call_identifier":"H2020","name":"Geometric study of Wasserstein spaces and free probability"},{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"doi":"10.1007/s11005-020-01282-0","language":[{"iso":"eng"}],"ec_funded":1,"year":"2020","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.","publication_status":"published","publisher":"Springer Nature","department":[{"_id":"LaEr"}],"author":[{"last_name":"Pitrik","first_name":"Jozsef","full_name":"Pitrik, Jozsef"},{"full_name":"Virosztek, Daniel","last_name":"Virosztek","first_name":"Daniel","orcid":"0000-0003-1109-5511","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2023-08-18T10:17:26Z","date_created":"2020-03-25T15:57:48Z","volume":110},{"publication_identifier":{"eissn":["15658538"],"issn":["00217670"]},"month":"11","doi":"10.1007/s11854-020-0135-2","language":[{"iso":"eng"}],"oa":1,"external_id":{"arxiv":["1804.11199"],"isi":["000611879400008"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.11199"}],"project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"quality_controlled":"1","isi":1,"ec_funded":1,"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"},{"first_name":"Kevin","last_name":"Schnelli","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin"}],"volume":142,"date_updated":"2023-08-24T11:16:03Z","date_created":"2021-02-07T23:01:15Z","year":"2020","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.","department":[{"_id":"LaEr"}],"publisher":"Springer Nature","publication_status":"published","article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2020-11-01T00:00:00Z","citation":{"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., & Schnelli, K. (2020). On the support of the free additive convolution. Journal d’Analyse Mathematique. Springer Nature. https://doi.org/10.1007/s11854-020-0135-2","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “On the support of the free additive convolution,” Journal d’Analyse Mathematique, vol. 142. Springer Nature, pp. 323–348, 2020.","ama":"Bao Z, Erdös L, Schnelli K. On the support of the free additive convolution. Journal d’Analyse Mathematique. 2020;142:323-348. doi:10.1007/s11854-020-0135-2","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “On the Support of the Free Additive Convolution.” Journal d’Analyse Mathematique. Springer Nature, 2020. https://doi.org/10.1007/s11854-020-0135-2.","mla":"Bao, Zhigang, et al. “On the Support of the Free Additive Convolution.” Journal d’Analyse Mathematique, vol. 142, Springer Nature, 2020, pp. 323–48, doi:10.1007/s11854-020-0135-2.","short":"Z. Bao, L. Erdös, K. Schnelli, Journal d’Analyse Mathematique 142 (2020) 323–348."},"publication":"Journal d'Analyse Mathematique","page":"323-348","article_type":"original","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]."}],"type":"journal_article","oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"9104","intvolume":" 142","title":"On the support of the free additive convolution","status":"public"},{"author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3036-1475","first_name":"Zhigang","last_name":"Bao","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"},{"last_name":"Schnelli","first_name":"Kevin","full_name":"Schnelli, Kevin"}],"date_created":"2022-03-18T10:18:59Z","date_updated":"2023-08-24T14:08:42Z","volume":279,"acknowledgement":"Partially supported by ERC Advanced Grant RANMAT No. 338804.","year":"2020","publication_status":"published","publisher":"Elsevier","department":[{"_id":"LaEr"}],"ec_funded":1,"article_number":"108639","doi":"10.1016/j.jfa.2020.108639","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.01597"}],"oa":1,"external_id":{"arxiv":["1708.01597"],"isi":["000559623200009"]},"quality_controlled":"1","isi":1,"project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"month":"10","publication_identifier":{"issn":["0022-1236"]},"oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"10862","status":"public","title":"Spectral rigidity for addition of random matrices at the regular edge","intvolume":" 279","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."}],"issue":"7","type":"journal_article","date_published":"2020-10-15T00:00:00Z","publication":"Journal of Functional Analysis","citation":{"mla":"Bao, Zhigang, et al. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” Journal of Functional Analysis, vol. 279, no. 7, 108639, Elsevier, 2020, doi:10.1016/j.jfa.2020.108639.","short":"Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 279 (2020).","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” Journal of Functional Analysis. Elsevier, 2020. https://doi.org/10.1016/j.jfa.2020.108639.","ama":"Bao Z, Erdös L, Schnelli K. Spectral rigidity for addition of random matrices at the regular edge. Journal of Functional Analysis. 2020;279(7). doi:10.1016/j.jfa.2020.108639","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.","apa":"Bao, Z., Erdös, L., & Schnelli, K. (2020). Spectral rigidity for addition of random matrices at the regular edge. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2020.108639","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Spectral rigidity for addition of random matrices at the regular edge,” Journal of Functional Analysis, vol. 279, no. 7. Elsevier, 2020."},"article_type":"original","day":"15","article_processing_charge":"No","scopus_import":"1","keyword":["Analysis"]},{"date_published":"2020-07-01T00:00:00Z","article_type":"original","publication":"Random Matrices: Theory and Application","citation":{"short":"G. Cipolloni, L. Erdös, Random Matrices: Theory and Application 9 (2020).","mla":"Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices: Theory and Application, vol. 9, no. 3, 2050006, World Scientific Publishing, 2020, doi:10.1142/S2010326320500069.","chicago":"Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices: Theory and Application. World Scientific Publishing, 2020. https://doi.org/10.1142/S2010326320500069.","ama":"Cipolloni G, Erdös L. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. 2020;9(3). doi:10.1142/S2010326320500069","apa":"Cipolloni, G., & Erdös, L. (2020). Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. World Scientific Publishing. https://doi.org/10.1142/S2010326320500069","ieee":"G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices,” Random Matrices: Theory and Application, vol. 9, no. 3. World Scientific Publishing, 2020.","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."},"day":"01","article_processing_charge":"No","scopus_import":"1","oa_version":"Preprint","status":"public","title":"Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices","intvolume":" 9","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6488","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."}],"issue":"3","type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1142/S2010326320500069","quality_controlled":"1","isi":1,"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"},{"name":"International IST Doctoral Program","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385"}],"external_id":{"arxiv":["1806.08751"],"isi":["000547464400001"]},"main_file_link":[{"url":"https://arxiv.org/abs/1806.08751","open_access":"1"}],"oa":1,"month":"07","publication_identifier":{"eissn":["20103271"],"issn":["20103263"]},"date_created":"2019-05-26T21:59:14Z","date_updated":"2023-08-28T08:38:48Z","volume":9,"author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","first_name":"Giorgio"},{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"}],"publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"World Scientific Publishing","year":"2020","ec_funded":1,"article_number":"2050006"},{"date_published":"2020-09-01T00:00:00Z","article_type":"original","page":"1203-1278","publication":"Communications in Mathematical Physics","citation":{"ama":"Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices I: Local law and the complex Hermitian case. Communications in Mathematical Physics. 2020;378:1203-1278. doi:10.1007/s00220-019-03657-4","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,” Communications in Mathematical Physics, vol. 378. Springer Nature, pp. 1203–1278, 2020.","apa":"Erdös, L., Krüger, T. H., & Schröder, D. J. (2020). Cusp universality for random matrices I: Local law and the complex Hermitian case. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03657-4","mla":"Erdös, László, et al. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” Communications in Mathematical Physics, vol. 378, Springer Nature, 2020, pp. 1203–78, doi:10.1007/s00220-019-03657-4.","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics 378 (2020) 1203–1278.","chicago":"Erdös, László, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” Communications in Mathematical Physics. Springer Nature, 2020. https://doi.org/10.1007/s00220-019-03657-4."},"day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","scopus_import":"1","file":[{"relation":"main_file","file_id":"8771","checksum":"c3a683e2afdcea27afa6880b01e53dc2","success":1,"date_updated":"2020-11-18T11:14:37Z","date_created":"2020-11-18T11:14:37Z","access_level":"open_access","file_name":"2020_CommMathPhysics_Erdoes.pdf","content_type":"application/pdf","file_size":2904574,"creator":"dernst"}],"oa_version":"Published Version","status":"public","title":"Cusp universality for random matrices I: Local law and the complex Hermitian case","ddc":["530","510"],"intvolume":" 378","_id":"6185","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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)."}],"type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1007/s00220-019-03657-4","quality_controlled":"1","isi":1,"project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"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":["000529483000001"],"arxiv":["1809.03971"]},"month":"09","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"date_updated":"2023-09-07T12:54:12Z","date_created":"2019-03-28T10:21:15Z","volume":378,"author":[{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","first_name":"Torben H","last_name":"Krüger","full_name":"Krüger, Torben H"},{"last_name":"Schröder","first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"6179"}]},"publication_status":"published","publisher":"Springer Nature","department":[{"_id":"LaEr"}],"year":"2020","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.","file_date_updated":"2020-11-18T11:14:37Z","ec_funded":1},{"month":"09","publication_identifier":{"issn":["1431-0635"],"eissn":["1431-0643"]},"quality_controlled":"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":["1804.07752"]},"oa":1,"language":[{"iso":"eng"}],"doi":"10.4171/dm/780","file_date_updated":"2023-12-18T10:42:32Z","publication_status":"published","publisher":"EMS Press","department":[{"_id":"LaEr"}],"year":"2020","date_created":"2023-12-18T10:37:43Z","date_updated":"2023-12-18T10:46:09Z","volume":25,"author":[{"last_name":"Alt","first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","full_name":"Alt, Johannes"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","full_name":"Erdös, László"},{"full_name":"Krüger, Torben H","last_name":"Krüger","first_name":"Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87"}],"related_material":{"record":[{"id":"6183","relation":"earlier_version","status":"public"}]},"keyword":["General Mathematics"],"day":"01","article_processing_charge":"Yes","has_accepted_license":"1","article_type":"original","page":"1421-1539","publication":"Documenta Mathematica","citation":{"apa":"Alt, J., Erdös, L., & Krüger, T. H. (2020). The Dyson equation with linear self-energy: Spectral bands, edges and cusps. Documenta Mathematica. EMS Press. https://doi.org/10.4171/dm/780","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy: Spectral bands, edges and cusps,” Documenta Mathematica, 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.","ama":"Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. Documenta Mathematica. 2020;25:1421-1539. doi:10.4171/dm/780","chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” Documenta Mathematica. EMS Press, 2020. https://doi.org/10.4171/dm/780.","short":"J. Alt, L. Erdös, T.H. Krüger, Documenta Mathematica 25 (2020) 1421–1539.","mla":"Alt, Johannes, et al. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” Documenta Mathematica, vol. 25, EMS Press, 2020, pp. 1421–539, doi:10.4171/dm/780."},"date_published":"2020-09-01T00:00:00Z","type":"journal_article","abstract":[{"lang":"eng","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."}],"ddc":["510"],"status":"public","title":"The Dyson equation with linear self-energy: Spectral bands, edges and cusps","intvolume":" 25","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"14694","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"14695","checksum":"12aacc1d63b852ff9a51c1f6b218d4a6","success":1,"date_created":"2023-12-18T10:42:32Z","date_updated":"2023-12-18T10:42:32Z","access_level":"open_access","file_name":"2020_DocumentaMathematica_Alt.pdf","file_size":1374708,"content_type":"application/pdf","creator":"dernst"}]},{"ec_funded":1,"publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"publication_status":"published","year":"2020","volume":48,"date_updated":"2024-02-22T14:34:33Z","date_created":"2019-03-28T09:20:08Z","related_material":{"record":[{"id":"149","relation":"dissertation_contains","status":"public"},{"status":"public","relation":"dissertation_contains","id":"6179"}]},"author":[{"full_name":"Alt, Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","last_name":"Alt","first_name":"Johannes"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"full_name":"Krüger, Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","first_name":"Torben H","last_name":"Krüger"},{"last_name":"Schröder","first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"publication_identifier":{"issn":["0091-1798"]},"month":"03","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"}],"quality_controlled":"1","isi":1,"external_id":{"arxiv":["1804.07744"],"isi":["000528269100013"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.07744"}],"language":[{"iso":"eng"}],"doi":"10.1214/19-AOP1379","type":"journal_article","issue":"2","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."}],"intvolume":" 48","title":"Correlated random matrices: Band rigidity and edge universality","status":"public","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","_id":"6184","oa_version":"Preprint","scopus_import":"1","article_processing_charge":"No","day":"01","page":"963-1001","article_type":"original","citation":{"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. Institute of Mathematical Statistics, pp. 963–1001, 2020.","apa":"Alt, J., Erdös, L., Krüger, T. H., & Schröder, D. J. (2020). Correlated random matrices: Band rigidity and edge universality. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/19-AOP1379","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.","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. doi:10.1214/19-AOP1379","chicago":"Alt, Johannes, László Erdös, Torben H Krüger, and Dominik J Schröder. “Correlated Random Matrices: Band Rigidity and Edge Universality.” Annals of Probability. Institute of Mathematical Statistics, 2020. https://doi.org/10.1214/19-AOP1379.","short":"J. Alt, L. Erdös, T.H. Krüger, D.J. Schröder, Annals of Probability 48 (2020) 963–1001.","mla":"Alt, Johannes, et al. “Correlated Random Matrices: Band Rigidity and Edge Universality.” Annals of Probability, vol. 48, no. 2, Institute of Mathematical Statistics, 2020, pp. 963–1001, doi:10.1214/19-AOP1379."},"publication":"Annals of Probability","date_published":"2020-03-01T00:00:00Z"},{"date_published":"2020-11-16T00:00:00Z","article_type":"original","page":"101-146","publication":"Probability and Mathematical Physics","citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. Optimal lower bound on the least singular value of the shifted Ginibre ensemble. Probability and Mathematical Physics. 2020;1(1):101-146. doi:10.2140/pmp.2020.1.101","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2020). Optimal lower bound on the least singular value of the shifted Ginibre ensemble. Probability and Mathematical Physics. Mathematical Sciences Publishers. https://doi.org/10.2140/pmp.2020.1.101","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal lower bound on the least singular value of the shifted Ginibre ensemble,” Probability and Mathematical Physics, vol. 1, no. 1. Mathematical Sciences Publishers, pp. 101–146, 2020.","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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability and Mathematical Physics 1 (2020) 101–146.","mla":"Cipolloni, Giorgio, et al. “Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble.” Probability and Mathematical Physics, vol. 1, no. 1, Mathematical Sciences Publishers, 2020, pp. 101–46, doi:10.2140/pmp.2020.1.101.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble.” Probability and Mathematical Physics. Mathematical Sciences Publishers, 2020. https://doi.org/10.2140/pmp.2020.1.101."},"day":"16","article_processing_charge":"No","keyword":["General Medicine"],"scopus_import":"1","oa_version":"Preprint","status":"public","title":"Optimal lower bound on the least singular value of the shifted Ginibre ensemble","intvolume":" 1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"15063","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"}],"issue":"1","type":"journal_article","language":[{"iso":"eng"}],"doi":"10.2140/pmp.2020.1.101","quality_controlled":"1","project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"},{"name":"International IST Doctoral Program","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385"}],"external_id":{"arxiv":["1908.01653"]},"oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1908.01653","open_access":"1"}],"month":"11","publication_identifier":{"issn":["2690-1005","2690-0998"]},"date_created":"2024-03-04T10:27:57Z","date_updated":"2024-03-04T10:33:15Z","volume":1,"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","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"},{"full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856"}],"publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Mathematical Sciences Publishers","year":"2020","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","ec_funded":1},{"publication_identifier":{"issn":["1660-8933"]},"article_processing_charge":"No","month":"11","day":"19","doi":"10.4171/owr/2019/56","date_published":"2020-11-19T00:00:00Z","language":[{"iso":"eng"}],"citation":{"chicago":"Erdös, László, Friedrich Götze, and Alice Guionnet. “Random Matrices.” Oberwolfach Reports. European Mathematical Society, 2020. https://doi.org/10.4171/owr/2019/56.","short":"L. Erdös, F. Götze, A. Guionnet, Oberwolfach Reports 16 (2020) 3459–3527.","mla":"Erdös, László, et al. “Random Matrices.” Oberwolfach Reports, vol. 16, no. 4, European Mathematical Society, 2020, pp. 3459–527, doi:10.4171/owr/2019/56.","ieee":"L. Erdös, F. Götze, and A. Guionnet, “Random matrices,” Oberwolfach Reports, vol. 16, no. 4. European Mathematical Society, pp. 3459–3527, 2020.","apa":"Erdös, L., Götze, F., & Guionnet, A. (2020). Random matrices. Oberwolfach Reports. European Mathematical Society. https://doi.org/10.4171/owr/2019/56","ista":"Erdös L, Götze F, Guionnet A. 2020. Random matrices. Oberwolfach Reports. 16(4), 3459–3527.","ama":"Erdös L, Götze F, Guionnet A. Random matrices. Oberwolfach Reports. 2020;16(4):3459-3527. doi:10.4171/owr/2019/56"},"publication":"Oberwolfach Reports","page":"3459-3527","article_type":"original","quality_controlled":"1","issue":"4","abstract":[{"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.","lang":"eng"}],"type":"journal_article","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"Erdös, László"},{"last_name":"Götze","first_name":"Friedrich","full_name":"Götze, Friedrich"},{"full_name":"Guionnet, Alice","first_name":"Alice","last_name":"Guionnet"}],"oa_version":"None","volume":16,"date_updated":"2024-03-12T12:25:18Z","date_created":"2024-03-05T07:54:44Z","_id":"15079","year":"2020","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"European Mathematical Society","intvolume":" 16","department":[{"_id":"LaEr"}],"title":"Random matrices","status":"public","publication_status":"published"},{"month":"01","day":"30","article_processing_charge":"No","quality_controlled":"1","page":"34-41","publication":"Kyoto RIMS Kôkyûroku","main_file_link":[{"open_access":"1","url":"http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/2125.html"}],"citation":{"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.","apa":"Geher, G. P., Titkos, T., & Virosztek, D. (2019). Dirac masses and isometric rigidity. In Kyoto RIMS Kôkyûroku (Vol. 2125, pp. 34–41). Kyoto, Japan: Research Institute for Mathematical Sciences, Kyoto University.","ieee":"G. P. Geher, T. Titkos, and D. Virosztek, “Dirac masses and isometric rigidity,” in Kyoto RIMS Kôkyûroku, Kyoto, Japan, 2019, vol. 2125, pp. 34–41.","ama":"Geher GP, Titkos T, Virosztek D. Dirac masses and isometric rigidity. In: Kyoto RIMS Kôkyûroku. 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 Kyoto RIMS Kôkyûroku, 2125:34–41. Research Institute for Mathematical Sciences, Kyoto University, 2019.","mla":"Geher, Gyorgy Pal, et al. “Dirac Masses and Isometric Rigidity.” Kyoto RIMS Kôkyûroku, vol. 2125, Research Institute for Mathematical Sciences, Kyoto University, 2019, pp. 34–41.","short":"G.P. Geher, T. Titkos, D. Virosztek, in:, Kyoto RIMS Kôkyûroku, Research Institute for Mathematical Sciences, Kyoto University, 2019, pp. 34–41."},"oa":1,"language":[{"iso":"eng"}],"conference":{"location":"Kyoto, Japan","start_date":"2019-01-28","end_date":"2019-01-30","name":"Research on isometries as preserver problems and related topics"},"date_published":"2019-01-30T00:00:00Z","type":"conference","abstract":[{"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.","lang":"eng"}],"title":"Dirac masses and isometric rigidity","status":"public","publication_status":"published","intvolume":" 2125","department":[{"_id":"LaEr"}],"publisher":"Research Institute for Mathematical Sciences, Kyoto University","_id":"7035","year":"2019","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2019-11-18T15:39:53Z","date_updated":"2021-01-12T08:11:33Z","volume":2125,"oa_version":"Submitted Version","author":[{"full_name":"Geher, Gyorgy Pal","last_name":"Geher","first_name":"Gyorgy Pal"},{"full_name":"Titkos, Tamas","first_name":"Tamas","last_name":"Titkos"},{"id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-1109-5511","first_name":"Daniel","last_name":"Virosztek","full_name":"Virosztek, Daniel"}]},{"month":"07","language":[{"iso":"eng"}],"conference":{"end_date":"2019-07-05","start_date":"2019-07-01","location":"Ljubljana, Slovenia","name":"FPSAC: International Conference on Formal Power Series and Algebraic Combinatorics"},"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"},{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"}],"quality_controlled":"1","main_file_link":[{"url":"https://arxiv.org/abs/1902.08750","open_access":"1"}],"external_id":{"arxiv":["1902.08750"]},"oa":1,"ec_funded":1,"article_number":"34","date_created":"2020-07-26T22:01:04Z","date_updated":"2021-01-12T08:17:18Z","author":[{"last_name":"Betea","first_name":"Dan","full_name":"Betea, Dan"},{"first_name":"Jérémie","last_name":"Bouttier","full_name":"Bouttier, Jérémie"},{"id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","last_name":"Nejjar","first_name":"Peter","full_name":"Nejjar, Peter"},{"full_name":"Vuletíc, Mirjana","last_name":"Vuletíc","first_name":"Mirjana"}],"department":[{"_id":"LaEr"}],"publisher":"Formal Power Series and Algebraic Combinatorics","publication_status":"published","year":"2019","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","article_processing_charge":"No","day":"01","scopus_import":"1","date_published":"2019-07-01T00:00:00Z","citation":{"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.","ieee":"D. Betea, J. Bouttier, P. Nejjar, and M. Vuletíc, “New edge asymptotics of skew Young diagrams via free boundaries,” in Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics, Ljubljana, Slovenia, 2019.","apa":"Betea, D., Bouttier, J., Nejjar, P., & Vuletíc, M. (2019). New edge asymptotics of skew Young diagrams via free boundaries. In Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. Ljubljana, Slovenia: Formal Power Series and Algebraic Combinatorics.","ama":"Betea D, Bouttier J, Nejjar P, Vuletíc M. New edge asymptotics of skew Young diagrams via free boundaries. 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 Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. Formal Power Series and Algebraic Combinatorics, 2019.","mla":"Betea, Dan, et al. “New Edge Asymptotics of Skew Young Diagrams via Free Boundaries.” Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics, 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."},"publication":"Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics","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."}],"type":"conference","oa_version":"Preprint","status":"public","title":"New edge asymptotics of skew Young diagrams via free boundaries","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"8175"},{"ec_funded":1,"publist_id":"7424","year":"2019","acknowledgement":"The author was supported by the ISTFELLOW program of the Institute of Science and Technology Austria (project code IC1027FELL01) and partially supported by the Hungarian National Research, Development and Innovation Office – NKFIH (grant no. K124152)","publication_status":"published","publisher":"Elsevier","department":[{"_id":"LaEr"}],"author":[{"orcid":"0000-0003-1109-5511","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","last_name":"Virosztek","first_name":"Daniel","full_name":"Virosztek, Daniel"}],"date_updated":"2023-08-24T14:31:47Z","date_created":"2018-12-11T11:46:17Z","volume":576,"month":"09","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1712.05324"}],"oa":1,"external_id":{"arxiv":["1712.05324"],"isi":["000470955300005"]},"quality_controlled":"1","isi":1,"project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"doi":"10.1016/j.laa.2018.03.002","language":[{"iso":"eng"}],"type":"journal_article","abstract":[{"lang":"eng","text":"We investigate the quantum Jensen divergences from the viewpoint of joint convexity. It turns out that the set of the functions which generate jointly convex quantum Jensen divergences on positive matrices coincides with the Matrix Entropy Class which has been introduced by Chen and Tropp quite recently."}],"_id":"405","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"Jointly convex quantum Jensen divergences","status":"public","intvolume":" 576","oa_version":"Preprint","scopus_import":"1","day":"01","article_processing_charge":"No","publication":"Linear Algebra and Its Applications","citation":{"ama":"Virosztek D. Jointly convex quantum Jensen divergences. Linear Algebra and Its Applications. 2019;576:67-78. doi:10.1016/j.laa.2018.03.002","ista":"Virosztek D. 2019. Jointly convex quantum Jensen divergences. Linear Algebra and Its Applications. 576, 67–78.","ieee":"D. Virosztek, “Jointly convex quantum Jensen divergences,” Linear Algebra and Its Applications, vol. 576. Elsevier, pp. 67–78, 2019.","apa":"Virosztek, D. (2019). Jointly convex quantum Jensen divergences. Linear Algebra and Its Applications. Elsevier. https://doi.org/10.1016/j.laa.2018.03.002","mla":"Virosztek, Daniel. “Jointly Convex Quantum Jensen Divergences.” Linear Algebra and Its Applications, vol. 576, Elsevier, 2019, pp. 67–78, doi:10.1016/j.laa.2018.03.002.","short":"D. Virosztek, Linear Algebra and Its Applications 576 (2019) 67–78.","chicago":"Virosztek, Daniel. “Jointly Convex Quantum Jensen Divergences.” Linear Algebra and Its Applications. Elsevier, 2019. https://doi.org/10.1016/j.laa.2018.03.002."},"article_type":"original","page":"67-78","date_published":"2019-09-01T00:00:00Z"},{"type":"journal_article","abstract":[{"lang":"eng","text":"We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay but are otherwise of general form. The key novelty is the detailed stability analysis of the corresponding matrix valued Dyson equation whose solution is the deterministic limit of the resolvent."}],"issue":"1-2","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"429","status":"public","title":"Stability of the matrix Dyson equation and random matrices with correlations","ddc":["510"],"intvolume":" 173","file":[{"file_name":"2018_ProbTheory_Ajanki.pdf","access_level":"open_access","content_type":"application/pdf","file_size":1201840,"creator":"dernst","relation":"main_file","file_id":"5720","date_created":"2018-12-17T16:12:08Z","date_updated":"2020-07-14T12:46:26Z","checksum":"f9354fa5c71f9edd17132588f0dc7d01"}],"oa_version":"Published Version","scopus_import":"1","day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","publication":"Probability Theory and Related Fields","citation":{"chicago":"Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Stability of the Matrix Dyson Equation and Random Matrices with Correlations.” Probability Theory and Related Fields. Springer, 2019. https://doi.org/10.1007/s00440-018-0835-z.","short":"O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields 173 (2019) 293–373.","mla":"Ajanki, Oskari H., et al. “Stability of the Matrix Dyson Equation and Random Matrices with Correlations.” Probability Theory and Related Fields, vol. 173, no. 1–2, Springer, 2019, pp. 293–373, doi:10.1007/s00440-018-0835-z.","ieee":"O. H. Ajanki, L. Erdös, and T. H. Krüger, “Stability of the matrix Dyson equation and random matrices with correlations,” Probability Theory and Related Fields, vol. 173, no. 1–2. Springer, pp. 293–373, 2019.","apa":"Ajanki, O. H., Erdös, L., & Krüger, T. H. (2019). Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-018-0835-z","ista":"Ajanki OH, Erdös L, Krüger TH. 2019. Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. 173(1–2), 293–373.","ama":"Ajanki OH, Erdös L, Krüger TH. Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. 2019;173(1-2):293–373. doi:10.1007/s00440-018-0835-z"},"article_type":"original","page":"293–373","date_published":"2019-02-01T00:00:00Z","file_date_updated":"2020-07-14T12:46:26Z","ec_funded":1,"publist_id":"7394","year":"2019","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).\r\n","publication_status":"published","publisher":"Springer","department":[{"_id":"LaEr"}],"author":[{"full_name":"Ajanki, Oskari H","id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87","first_name":"Oskari H","last_name":"Ajanki"},{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Krüger, Torben H","last_name":"Krüger","first_name":"Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2023-08-24T14:39:00Z","date_created":"2018-12-11T11:46:25Z","volume":173,"month":"02","publication_identifier":{"issn":["01788051"],"eissn":["14322064"]},"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":{"isi":["000459396500007"]},"isi":1,"quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"doi":"10.1007/s00440-018-0835-z","language":[{"iso":"eng"}]},{"day":"01","article_processing_charge":"No","scopus_import":"1","date_published":"2019-04-01T00:00:00Z","page":"1082-1098","publication":"Ergodic Theory and Dynamical Systems","citation":{"ista":"Sadel C, Xu D. 2019. Singular analytic linear cocycles with negative infinite Lyapunov exponents. Ergodic Theory and Dynamical Systems. 39(4), 1082–1098.","apa":"Sadel, C., & Xu, D. (2019). Singular analytic linear cocycles with negative infinite Lyapunov exponents. Ergodic Theory and Dynamical Systems. Cambridge University Press. https://doi.org/10.1017/etds.2017.52","ieee":"C. Sadel and D. Xu, “Singular analytic linear cocycles with negative infinite Lyapunov exponents,” Ergodic Theory and Dynamical Systems, vol. 39, no. 4. Cambridge University Press, pp. 1082–1098, 2019.","ama":"Sadel C, Xu D. Singular analytic linear cocycles with negative infinite Lyapunov exponents. Ergodic Theory and Dynamical Systems. 2019;39(4):1082-1098. doi:10.1017/etds.2017.52","chicago":"Sadel, Christian, and Disheng Xu. “Singular Analytic Linear Cocycles with Negative Infinite Lyapunov Exponents.” Ergodic Theory and Dynamical Systems. Cambridge University Press, 2019. https://doi.org/10.1017/etds.2017.52.","mla":"Sadel, Christian, and Disheng Xu. “Singular Analytic Linear Cocycles with Negative Infinite Lyapunov Exponents.” Ergodic Theory and Dynamical Systems, vol. 39, no. 4, Cambridge University Press, 2019, pp. 1082–98, doi:10.1017/etds.2017.52.","short":"C. Sadel, D. Xu, Ergodic Theory and Dynamical Systems 39 (2019) 1082–1098."},"abstract":[{"lang":"eng","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."}],"issue":"4","type":"journal_article","oa_version":"Preprint","title":"Singular analytic linear cocycles with negative infinite Lyapunov exponents","status":"public","intvolume":" 39","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6086","month":"04","language":[{"iso":"eng"}],"doi":"10.1017/etds.2017.52","isi":1,"quality_controlled":"1","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1601.06118"}],"oa":1,"external_id":{"arxiv":["1601.06118"],"isi":["000459725600012"]},"ec_funded":1,"date_updated":"2023-08-25T08:03:30Z","date_created":"2019-03-10T22:59:18Z","volume":39,"author":[{"id":"4760E9F8-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-8255-3968","first_name":"Christian","last_name":"Sadel","full_name":"Sadel, Christian"},{"first_name":"Disheng","last_name":"Xu","full_name":"Xu, Disheng"}],"publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Cambridge University Press","year":"2019"},{"type":"journal_article","issue":"3","abstract":[{"lang":"eng","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)."}],"_id":"6511","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 47","status":"public","title":"Local single ring theorem on optimal scale","oa_version":"Preprint","scopus_import":"1","article_processing_charge":"No","day":"01","citation":{"mla":"Bao, Zhigang, et al. “Local Single Ring Theorem on Optimal Scale.” Annals of Probability, vol. 47, no. 3, Institute of Mathematical Statistics, 2019, pp. 1270–334, doi:10.1214/18-AOP1284.","short":"Z. Bao, L. Erdös, K. Schnelli, Annals of Probability 47 (2019) 1270–1334.","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Single Ring Theorem on Optimal Scale.” Annals of Probability. Institute of Mathematical Statistics, 2019. https://doi.org/10.1214/18-AOP1284.","ama":"Bao Z, Erdös L, Schnelli K. Local single ring theorem on optimal scale. Annals of Probability. 2019;47(3):1270-1334. doi:10.1214/18-AOP1284","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,” Annals of Probability, vol. 47, no. 3. Institute of Mathematical Statistics, pp. 1270–1334, 2019.","apa":"Bao, Z., Erdös, L., & Schnelli, K. (2019). Local single ring theorem on optimal scale. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/18-AOP1284"},"publication":"Annals of Probability","page":"1270-1334","date_published":"2019-05-01T00:00:00Z","ec_funded":1,"year":"2019","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","publication_status":"published","author":[{"full_name":"Bao, Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3036-1475","first_name":"Zhigang","last_name":"Bao"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"full_name":"Schnelli, Kevin","orcid":"0000-0003-0954-3231","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","last_name":"Schnelli","first_name":"Kevin"}],"volume":47,"date_created":"2019-06-02T21:59:13Z","date_updated":"2023-08-28T09:32:29Z","publication_identifier":{"issn":["00911798"]},"month":"05","oa":1,"external_id":{"arxiv":["1612.05920"],"isi":["000466616100003"]},"main_file_link":[{"url":"https://arxiv.org/abs/1612.05920","open_access":"1"}],"project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"quality_controlled":"1","isi":1,"doi":"10.1214/18-AOP1284","language":[{"iso":"eng"}]},{"ec_funded":1,"article_number":"123435","author":[{"full_name":"Gehér, György Pál","first_name":"György Pál","last_name":"Gehér"},{"full_name":"Titkos, Tamás","last_name":"Titkos","first_name":"Tamás"},{"first_name":"Daniel","last_name":"Virosztek","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel"}],"volume":480,"date_updated":"2023-08-29T07:18:50Z","date_created":"2019-09-01T22:01:01Z","year":"2019","department":[{"_id":"LaEr"}],"publisher":"Elsevier","publication_status":"published","publication_identifier":{"eissn":["10960813"],"issn":["0022247X"]},"month":"12","doi":"10.1016/j.jmaa.2019.123435","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1809.01101"}],"external_id":{"isi":["000486563900031"],"arxiv":["1809.01101"]},"oa":1,"project":[{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"isi":1,"quality_controlled":"1","issue":"2","abstract":[{"lang":"eng","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
Journal of Mathematical Analysis and Applications. Elsevier, 2019. https://doi.org/10.1016/j.jmaa.2019.123435.","mla":"Gehér, György Pál, et al. “On Isometric Embeddings of Wasserstein Spaces – the Discrete Case.” Journal of Mathematical Analysis and Applications, vol. 480, no. 2, 123435, Elsevier, 2019, doi:10.1016/j.jmaa.2019.123435.","short":"G.P. Gehér, T. Titkos, D. Virosztek, Journal of Mathematical Analysis and Applications 480 (2019).","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.","apa":"Gehér, G. P., Titkos, T., & Virosztek, D. (2019). On isometric embeddings of Wasserstein spaces – the discrete case. Journal of Mathematical Analysis and Applications. Elsevier. https://doi.org/10.1016/j.jmaa.2019.123435","ieee":"G. P. Gehér, T. Titkos, and D. Virosztek, “On isometric embeddings of Wasserstein spaces – the discrete case,” Journal of Mathematical Analysis and Applications, vol. 480, no. 2. Elsevier, 2019.","ama":"Gehér GP, Titkos T, Virosztek D. On isometric embeddings of Wasserstein spaces – the discrete case. Journal of Mathematical Analysis and Applications. 2019;480(2). doi:10.1016/j.jmaa.2019.123435"},"publication":"Journal of Mathematical Analysis and Applications","article_type":"original"},{"_id":"7423","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","intvolume":" 55","title":"Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles","status":"public","oa_version":"Preprint","type":"journal_article","issue":"1","abstract":[{"lang":"eng","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."}],"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. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. 2019;55(1):441-479. doi:10.1214/18-aihp888","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,” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, vol. 55, no. 1. Institute of Mathematical Statistics, pp. 441–479, 2019.","apa":"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. Institute of Mathematical Statistics. https://doi.org/10.1214/18-aihp888","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.","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.” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, vol. 55, no. 1, Institute of Mathematical Statistics, 2019, pp. 441–79, doi:10.1214/18-aihp888.","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.” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. Institute of Mathematical Statistics, 2019. https://doi.org/10.1214/18-aihp888."},"publication":"Annales de l'Institut Henri Poincaré, Probabilités et Statistiques","page":"441-479","article_type":"original","date_published":"2019-02-01T00:00:00Z","article_processing_charge":"No","day":"01","year":"2019","publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"publication_status":"published","author":[{"first_name":"Gernot","last_name":"Akemann","full_name":"Akemann, Gernot"},{"first_name":"Tomasz","last_name":"Checinski","full_name":"Checinski, Tomasz"},{"full_name":"Liu, Dangzheng","last_name":"Liu","first_name":"Dangzheng","id":"2F947E34-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Strahov, Eugene","last_name":"Strahov","first_name":"Eugene"}],"volume":55,"date_updated":"2023-09-06T14:58:39Z","date_created":"2020-01-30T10:36:50Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1704.05224"}],"oa":1,"external_id":{"isi":["000456070200013"],"arxiv":["1704.05224"]},"isi":1,"quality_controlled":"1","doi":"10.1214/18-aihp888","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0246-0203"]},"month":"02"},{"citation":{"mla":"Erdös, László, et al. “Random Matrices with Slow Correlation Decay.” Forum of Mathematics, Sigma, vol. 7, e8, Cambridge University Press, 2019, doi:10.1017/fms.2019.2.","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Forum of Mathematics, Sigma 7 (2019).","chicago":"Erdös, László, Torben H Krüger, and Dominik J Schröder. “Random Matrices with Slow Correlation Decay.” Forum of Mathematics, Sigma. Cambridge University Press, 2019. https://doi.org/10.1017/fms.2019.2.","ama":"Erdös L, Krüger TH, Schröder DJ. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 2019;7. doi:10.1017/fms.2019.2","ista":"Erdös L, Krüger TH, Schröder DJ. 2019. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 7, e8.","apa":"Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Random matrices with slow correlation decay. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2019.2","ieee":"L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation decay,” Forum of Mathematics, Sigma, vol. 7. Cambridge University Press, 2019."},"publication":"Forum of Mathematics, Sigma","article_type":"original","date_published":"2019-03-26T00:00:00Z","scopus_import":"1","article_processing_charge":"No","has_accepted_license":"1","day":"26","_id":"6182","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":" 7","title":"Random matrices with slow correlation decay","ddc":["510"],"status":"public","oa_version":"Published Version","file":[{"access_level":"open_access","file_name":"2019_Forum_Erdoes.pdf","creator":"dernst","content_type":"application/pdf","file_size":1520344,"file_id":"6883","relation":"main_file","checksum":"933a472568221c73b2c3ce8c87bf6d15","date_updated":"2020-07-14T12:47:22Z","date_created":"2019-09-17T14:24:13Z"}],"type":"journal_article","abstract":[{"lang":"eng","text":"We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the recent result of Ajanki et al. [‘Stability of the matrix Dyson equation and random matrices with correlations’, Probab. Theory Related Fields 173(1–2) (2019), 293–373] to allow slow correlation decay and arbitrary expectation. The main novel tool is\r\na systematic diagrammatic control of a multivariate cumulant expansion."}],"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":["000488847100001"],"arxiv":["1705.10661"]},"oa":1,"project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"quality_controlled":"1","isi":1,"doi":"10.1017/fms.2019.2","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["20505094"]},"month":"03","year":"2019","publisher":"Cambridge University Press","department":[{"_id":"LaEr"}],"publication_status":"published","related_material":{"record":[{"id":"6179","status":"public","relation":"dissertation_contains"}]},"author":[{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Krüger, Torben H","first_name":"Torben H","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","first_name":"Dominik J","last_name":"Schröder","full_name":"Schröder, Dominik J"}],"volume":7,"date_created":"2019-03-28T09:05:23Z","date_updated":"2023-09-07T12:54:12Z","article_number":"e8","ec_funded":1,"file_date_updated":"2020-07-14T12:47:22Z"},{"publication_identifier":{"eissn":["2578-5885"],"issn":["2578-5893"]},"month":"10","doi":"10.2140/paa.2019.1.615","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1811.04055","open_access":"1"}],"external_id":{"arxiv":["1811.04055"]},"project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"name":"International IST Doctoral Program","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385"}],"quality_controlled":"1","ec_funded":1,"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"6179"}]},"author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","first_name":"Giorgio","last_name":"Cipolloni"},{"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":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","first_name":"Dominik J"}],"volume":1,"date_created":"2019-03-28T10:21:17Z","date_updated":"2023-09-07T12:54:12Z","year":"2019","publisher":"MSP","department":[{"_id":"LaEr"}],"publication_status":"published","article_processing_charge":"No","day":"12","date_published":"2019-10-12T00:00:00Z","citation":{"apa":"Cipolloni, G., Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . MSP. https://doi.org/10.2140/paa.2019.1.615","ieee":"G. Cipolloni, L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices, II: The real symmetric case,” Pure and Applied Analysis , vol. 1, no. 4. MSP, pp. 615–707, 2019.","ista":"Cipolloni G, Erdös L, Krüger TH, Schröder DJ. 2019. Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . 1(4), 615–707.","ama":"Cipolloni G, Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . 2019;1(4):615–707. doi:10.2140/paa.2019.1.615","chicago":"Cipolloni, Giorgio, László Erdös, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” Pure and Applied Analysis . MSP, 2019. https://doi.org/10.2140/paa.2019.1.615.","short":"G. Cipolloni, L. Erdös, T.H. Krüger, D.J. Schröder, Pure and Applied Analysis 1 (2019) 615–707.","mla":"Cipolloni, Giorgio, et al. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” Pure and Applied Analysis , vol. 1, no. 4, MSP, 2019, pp. 615–707, doi:10.2140/paa.2019.1.615."},"publication":"Pure and Applied Analysis ","page":"615–707","article_type":"original","issue":"4","abstract":[{"text":"We prove that the local eigenvalue statistics of real symmetric Wigner-type\r\nmatrices near the cusp points of the eigenvalue density are universal. Together\r\nwith the companion paper [arXiv:1809.03971], which proves the same result for\r\nthe complex Hermitian symmetry class, this completes the last remaining case of\r\nthe Wigner-Dyson-Mehta universality conjecture after bulk and edge\r\nuniversalities have been established in the last years. We extend the recent\r\nDyson Brownian motion analysis at the edge [arXiv:1712.03881] to the cusp\r\nregime using the optimal local law from [arXiv:1809.03971] and the accurate\r\nlocal shape analysis of the density from [arXiv:1506.05095, arXiv:1804.07752].\r\nWe also present a PDE-based method to improve the estimate on eigenvalue\r\nrigidity via the maximum principle of the heat flow related to the Dyson\r\nBrownian motion.","lang":"eng"}],"type":"journal_article","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"6186","intvolume":" 1","status":"public","title":"Cusp universality for random matrices, II: The real symmetric case"},{"type":"journal_article","issue":"3","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."}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"10879","intvolume":" 9","status":"public","title":"Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function","oa_version":"Preprint","scopus_import":"1","keyword":["Random Schrödinger operators","spectral shift function","Anderson orthogonality"],"article_processing_charge":"No","day":"01","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.","apa":"Dietlein, A. M., 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. European Mathematical Society Publishing House. https://doi.org/10.4171/jst/267","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,” Journal of Spectral Theory, vol. 9, no. 3. European Mathematical Society Publishing House, pp. 921–965, 2019.","ama":"Dietlein AM, Gebert M, Müller P. Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function. Journal of Spectral Theory. 2019;9(3):921-965. doi:10.4171/jst/267","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.” Journal of Spectral Theory. European Mathematical Society Publishing House, 2019. https://doi.org/10.4171/jst/267.","mla":"Dietlein, Adrian M., et al. “Perturbations of Continuum Random Schrödinger Operators with Applications to Anderson Orthogonality and the Spectral Shift Function.” Journal of Spectral Theory, vol. 9, no. 3, European Mathematical Society Publishing House, 2019, pp. 921–65, doi:10.4171/jst/267.","short":"A.M. Dietlein, M. Gebert, P. Müller, Journal of Spectral Theory 9 (2019) 921–965."},"publication":"Journal of Spectral Theory","page":"921-965","article_type":"original","date_published":"2019-03-01T00:00:00Z","acknowledgement":"M.G. was supported by the DFG under grant GE 2871/1-1.","year":"2019","department":[{"_id":"LaEr"}],"publisher":"European Mathematical Society Publishing House","publication_status":"published","author":[{"id":"317CB464-F248-11E8-B48F-1D18A9856A87","last_name":"Dietlein","first_name":"Adrian M","full_name":"Dietlein, Adrian M"},{"full_name":"Gebert, Martin","first_name":"Martin","last_name":"Gebert"},{"first_name":"Peter","last_name":"Müller","full_name":"Müller, Peter"}],"volume":9,"date_updated":"2023-09-08T11:35:31Z","date_created":"2022-03-18T12:36:42Z","publication_identifier":{"issn":["1664-039X"]},"month":"03","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1701.02956"}],"oa":1,"external_id":{"arxiv":["1701.02956"],"isi":["000484709400006"]},"quality_controlled":"1","isi":1,"doi":"10.4171/jst/267","language":[{"iso":"eng"}]},{"date_published":"2019-09-25T00:00:00Z","article_type":"original","page":"1203-1225","publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","citation":{"chicago":"Ferrari, Patrick, Promit Ghosal, and Peter Nejjar. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics, 2019. https://doi.org/10.1214/18-AIHP916.","mla":"Ferrari, Patrick, et al. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 55, no. 3, Institute of Mathematical Statistics, 2019, pp. 1203–25, doi:10.1214/18-AIHP916.","short":"P. Ferrari, P. Ghosal, P. Nejjar, Annales de l’institut Henri Poincare (B) Probability and Statistics 55 (2019) 1203–1225.","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.","ieee":"P. Ferrari, P. Ghosal, and P. Nejjar, “Limit law of a second class particle in TASEP with non-random initial condition,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 55, no. 3. Institute of Mathematical Statistics, pp. 1203–1225, 2019.","apa":"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. Institute of Mathematical Statistics. https://doi.org/10.1214/18-AIHP916","ama":"Ferrari P, Ghosal P, Nejjar P. Limit law of a second class particle in TASEP with non-random initial condition. Annales de l’institut Henri Poincare (B) Probability and Statistics. 2019;55(3):1203-1225. doi:10.1214/18-AIHP916"},"day":"25","article_processing_charge":"No","scopus_import":"1","oa_version":"Preprint","status":"public","title":"Limit law of a second class particle in TASEP with non-random initial condition","intvolume":" 55","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"72","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<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."}],"issue":"3","type":"journal_article","language":[{"iso":"eng"}],"doi":"10.1214/18-AIHP916","quality_controlled":"1","isi":1,"project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"},{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1710.02323"}],"oa":1,"external_id":{"isi":["000487763200001"],"arxiv":["1710.02323"]},"month":"09","publication_identifier":{"issn":["0246-0203"]},"date_created":"2018-12-11T11:44:29Z","date_updated":"2023-10-17T08:53:45Z","volume":55,"author":[{"full_name":"Ferrari, Patrick","first_name":"Patrick","last_name":"Ferrari"},{"first_name":"Promit","last_name":"Ghosal","full_name":"Ghosal, Promit"},{"first_name":"Peter","last_name":"Nejjar","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","full_name":"Nejjar, Peter"}],"publication_status":"published","publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"year":"2019","ec_funded":1},{"day":"01","article_processing_charge":"No","scopus_import":"1","date_published":"2019-05-01T00:00:00Z","page":"661-696","publication":"Annales de l'institut Henri Poincare","citation":{"mla":"Alt, Johannes, et al. “Location of the Spectrum of Kronecker Random Matrices.” Annales de l’institut Henri Poincare, vol. 55, no. 2, Institut Henri Poincaré, 2019, pp. 661–96, doi:10.1214/18-AIHP894.","short":"J. Alt, L. Erdös, T.H. Krüger, Y. Nemish, Annales de l’institut Henri Poincare 55 (2019) 661–696.","chicago":"Alt, Johannes, László Erdös, Torben H Krüger, and Yuriy Nemish. “Location of the Spectrum of Kronecker Random Matrices.” Annales de l’institut Henri Poincare. Institut Henri Poincaré, 2019. https://doi.org/10.1214/18-AIHP894.","ama":"Alt J, Erdös L, Krüger TH, Nemish Y. Location of the spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare. 2019;55(2):661-696. doi:10.1214/18-AIHP894","ista":"Alt J, Erdös L, Krüger TH, Nemish Y. 2019. Location of the spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare. 55(2), 661–696.","apa":"Alt, J., Erdös, L., Krüger, T. H., & Nemish, Y. (2019). Location of the spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare. Institut Henri Poincaré. https://doi.org/10.1214/18-AIHP894","ieee":"J. Alt, L. Erdös, T. H. Krüger, and Y. Nemish, “Location of the spectrum of Kronecker random matrices,” Annales de l’institut Henri Poincare, vol. 55, no. 2. Institut Henri Poincaré, pp. 661–696, 2019."},"abstract":[{"text":"For a general class of large non-Hermitian random block matrices X we prove that there are no eigenvalues away from a deterministic set with very high probability. This set is obtained from the Dyson equation of the Hermitization of X as the self-consistent approximation of the pseudospectrum. We demonstrate that the analysis of the matrix Dyson equation from (Probab. Theory Related Fields (2018)) offers a unified treatment of many structured matrix ensembles.","lang":"eng"}],"issue":"2","type":"journal_article","oa_version":"Preprint","status":"public","title":"Location of the spectrum of Kronecker random matrices","intvolume":" 55","_id":"6240","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"05","publication_identifier":{"issn":["0246-0203"]},"language":[{"iso":"eng"}],"doi":"10.1214/18-AIHP894","quality_controlled":"1","isi":1,"project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"oa":1,"external_id":{"arxiv":["1706.08343"],"isi":["000467793600003"]},"main_file_link":[{"url":"https://arxiv.org/abs/1706.08343","open_access":"1"}],"ec_funded":1,"date_updated":"2023-10-17T12:20:20Z","date_created":"2019-04-08T14:05:04Z","volume":55,"author":[{"full_name":"Alt, Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","last_name":"Alt","first_name":"Johannes"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"},{"full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","last_name":"Krüger","first_name":"Torben H"},{"orcid":"0000-0002-7327-856X","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","last_name":"Nemish","first_name":"Yuriy","full_name":"Nemish, Yuriy"}],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"149"}]},"publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Institut Henri Poincaré","year":"2019"},{"file":[{"content_type":"application/x-gzip","file_size":7104482,"creator":"dernst","file_name":"2019_Schroeder_Thesis.tar.gz","access_level":"closed","date_created":"2019-03-28T08:53:52Z","date_updated":"2020-07-14T12:47:21Z","checksum":"6926f66f28079a81c4937e3764be00fc","relation":"source_file","file_id":"6180"},{"file_name":"2019_Schroeder_Thesis.pdf","access_level":"open_access","content_type":"application/pdf","file_size":4228794,"creator":"dernst","relation":"main_file","file_id":"6181","date_updated":"2020-07-14T12:47:21Z","date_created":"2019-03-28T08:53:52Z","checksum":"7d0ebb8d1207e89768cdd497a5bf80fb"}],"oa_version":"Published Version","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"6179","title":"From Dyson to Pearcey: Universal statistics in random matrix theory","ddc":["515","519"],"status":"public","abstract":[{"lang":"eng","text":"In the first part of this thesis we consider large random matrices with arbitrary expectation and a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent in the bulk and edge regime. The main novel tool is a systematic diagrammatic control of a multivariate cumulant expansion.\r\nIn the second part we consider Wigner-type matrices and show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are uni- versal 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. Our analysis holds not only for exact cusps, but approximate cusps as well, where an ex- tended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp, and extend the fast relaxation to equilibrium of the Dyson Brow- nian motion to the cusp regime.\r\nIn the third and final part we explore the entrywise linear statistics of Wigner ma- trices and identify the fluctuations for a large class of test functions with little regularity. This enables us to study the rectangular Young diagram obtained from the interlacing eigenvalues of the random matrix and its minor, and we find that, despite having the same limit, the fluctuations differ from those of the algebraic Young tableaux equipped with the Plancharel measure."}],"type":"dissertation","alternative_title":["ISTA Thesis"],"date_published":"2019-03-18T00:00:00Z","citation":{"chicago":"Schröder, Dominik J. “From Dyson to Pearcey: Universal Statistics in Random Matrix Theory.” Institute of Science and Technology Austria, 2019. https://doi.org/10.15479/AT:ISTA:th6179.","mla":"Schröder, Dominik J. From Dyson to Pearcey: Universal Statistics in Random Matrix Theory. Institute of Science and Technology Austria, 2019, doi:10.15479/AT:ISTA:th6179.","short":"D.J. Schröder, From Dyson to Pearcey: Universal Statistics in Random Matrix Theory, Institute of Science and Technology Austria, 2019.","ista":"Schröder DJ. 2019. From Dyson to Pearcey: Universal statistics in random matrix theory. Institute of Science and Technology Austria.","apa":"Schröder, D. J. (2019). From Dyson to Pearcey: Universal statistics in random matrix theory. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th6179","ieee":"D. J. Schröder, “From Dyson to Pearcey: Universal statistics in random matrix theory,” Institute of Science and Technology Austria, 2019.","ama":"Schröder DJ. From Dyson to Pearcey: Universal statistics in random matrix theory. 2019. doi:10.15479/AT:ISTA:th6179"},"page":"375","article_processing_charge":"No","has_accepted_license":"1","day":"18","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"1144"},{"relation":"part_of_dissertation","status":"public","id":"6186"},{"id":"6185","status":"public","relation":"part_of_dissertation"},{"id":"6182","status":"public","relation":"part_of_dissertation"},{"id":"1012","status":"public","relation":"part_of_dissertation"},{"status":"public","relation":"part_of_dissertation","id":"6184"}]},"author":[{"last_name":"Schröder","first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"date_updated":"2024-02-22T14:34:33Z","date_created":"2019-03-28T08:58:59Z","year":"2019","department":[{"_id":"LaEr"}],"publisher":"Institute of Science and Technology Austria","publication_status":"published","ec_funded":1,"file_date_updated":"2020-07-14T12:47:21Z","doi":"10.15479/AT:ISTA:th6179","language":[{"iso":"eng"}],"degree_awarded":"PhD","supervisor":[{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"}],"oa":1,"project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"publication_identifier":{"issn":["2663-337X"]},"month":"03"},{"issue":"1-2","abstract":[{"text":"We consider spectral properties and the edge universality of sparse random matrices, the class of random matrices that includes the adjacency matrices of the Erdős–Rényi graph model G(N, p). We prove a local law for the eigenvalue density up to the spectral edges. Under a suitable condition on the sparsity, we also prove that the rescaled extremal eigenvalues exhibit GOE Tracy–Widom fluctuations if a deterministic shift of the spectral edge due to the sparsity is included. For the adjacency matrix of the Erdős–Rényi graph this establishes the Tracy–Widom fluctuations of the second largest eigenvalue when p is much larger than N−2/3 with a deterministic shift of order (Np)−1.","lang":"eng"}],"type":"journal_article","oa_version":"Preprint","intvolume":" 171","status":"public","title":"Local law and Tracy–Widom limit for sparse random matrices","_id":"690","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"14","scopus_import":1,"date_published":"2018-06-14T00:00:00Z","citation":{"mla":"Lee, Jii, and Kevin Schnelli. “Local Law and Tracy–Widom Limit for Sparse Random Matrices.” Probability Theory and Related Fields, vol. 171, no. 1–2, 543–616, Springer, 2018, doi:10.1007/s00440-017-0787-8.","short":"J. Lee, K. Schnelli, Probability Theory and Related Fields 171 (2018).","chicago":"Lee, Jii, and Kevin Schnelli. “Local Law and Tracy–Widom Limit for Sparse Random Matrices.” Probability Theory and Related Fields. Springer, 2018. https://doi.org/10.1007/s00440-017-0787-8.","ama":"Lee J, Schnelli K. Local law and Tracy–Widom limit for sparse random matrices. Probability Theory and Related Fields. 2018;171(1-2). doi:10.1007/s00440-017-0787-8","ista":"Lee J, Schnelli K. 2018. Local law and Tracy–Widom limit for sparse random matrices. Probability Theory and Related Fields. 171(1–2), 543–616.","apa":"Lee, J., & Schnelli, K. (2018). Local law and Tracy–Widom limit for sparse random matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-017-0787-8","ieee":"J. Lee and K. Schnelli, “Local law and Tracy–Widom limit for sparse random matrices,” Probability Theory and Related Fields, vol. 171, no. 1–2. Springer, 2018."},"publication":"Probability Theory and Related Fields","publist_id":"7017","ec_funded":1,"article_number":"543-616","volume":171,"date_created":"2018-12-11T11:47:56Z","date_updated":"2021-01-12T08:09:33Z","author":[{"last_name":"Lee","first_name":"Jii","full_name":"Lee, Jii"},{"full_name":"Schnelli, Kevin","last_name":"Schnelli","first_name":"Kevin","orcid":"0000-0003-0954-3231","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87"}],"publisher":"Springer","department":[{"_id":"LaEr"}],"publication_status":"published","year":"2018","month":"06","language":[{"iso":"eng"}],"doi":"10.1007/s00440-017-0787-8","project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1605.08767"}],"oa":1,"external_id":{"arxiv":["1605.08767"]}},{"scopus_import":"1","article_processing_charge":"No","day":"03","page":"148-203","article_type":"original","citation":{"ista":"Alt J, Erdös L, Krüger TH. 2018. Local inhomogeneous circular law. Annals Applied Probability . 28(1), 148–203.","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “Local inhomogeneous circular law,” Annals Applied Probability , vol. 28, no. 1. Institute of Mathematical Statistics, pp. 148–203, 2018.","apa":"Alt, J., Erdös, L., & Krüger, T. H. (2018). Local inhomogeneous circular law. Annals Applied Probability . Institute of Mathematical Statistics. https://doi.org/10.1214/17-AAP1302","ama":"Alt J, Erdös L, Krüger TH. Local inhomogeneous circular law. Annals Applied Probability . 2018;28(1):148-203. doi:10.1214/17-AAP1302","chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “Local Inhomogeneous Circular Law.” Annals Applied Probability . Institute of Mathematical Statistics, 2018. https://doi.org/10.1214/17-AAP1302.","mla":"Alt, Johannes, et al. “Local Inhomogeneous Circular Law.” Annals Applied Probability , vol. 28, no. 1, Institute of Mathematical Statistics, 2018, pp. 148–203, doi:10.1214/17-AAP1302.","short":"J. Alt, L. Erdös, T.H. Krüger, Annals Applied Probability 28 (2018) 148–203."},"publication":"Annals Applied Probability ","date_published":"2018-03-03T00:00:00Z","type":"journal_article","issue":"1","abstract":[{"lang":"eng","text":"We consider large random matrices X with centered, independent entries which have comparable but not necessarily identical variances. Girko's circular law asserts that the spectrum is supported in a disk and in case of identical variances, the limiting density is uniform. In this special case, the local circular law by Bourgade et. al. [11,12] shows that the empirical density converges even locally on scales slightly above the typical eigenvalue spacing. In the general case, the limiting density is typically inhomogeneous and it is obtained via solving a system of deterministic equations. Our main result is the local inhomogeneous circular law in the bulk spectrum on the optimal scale for a general variance profile of the entries of X. \r\n\r\n"}],"intvolume":" 28","title":"Local inhomogeneous circular law","status":"public","_id":"566","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Preprint","month":"03","project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"quality_controlled":"1","isi":1,"oa":1,"external_id":{"isi":["000431721800005"],"arxiv":["1612.07776 "]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1612.07776 "}],"language":[{"iso":"eng"}],"doi":"10.1214/17-AAP1302","ec_funded":1,"publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"publication_status":"published","year":"2018","volume":28,"date_created":"2018-12-11T11:47:13Z","date_updated":"2023-09-13T08:47:52Z","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"149"}]},"author":[{"full_name":"Alt, Johannes","first_name":"Johannes","last_name":"Alt","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"},{"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"}]},{"date_published":"2018-01-01T00:00:00Z","publication":"SIAM Journal on Mathematical Analysis","citation":{"chicago":"Erdös, László, Torben H Krüger, and David T Renfrew. “Power Law Decay for Systems of Randomly Coupled Differential Equations.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/17M1143125.","short":"L. Erdös, T.H. Krüger, D.T. Renfrew, SIAM Journal on Mathematical Analysis 50 (2018) 3271–3290.","mla":"Erdös, László, et al. “Power Law Decay for Systems of Randomly Coupled Differential Equations.” SIAM Journal on Mathematical Analysis, vol. 50, no. 3, Society for Industrial and Applied Mathematics , 2018, pp. 3271–90, doi:10.1137/17M1143125.","apa":"Erdös, L., Krüger, T. H., & Renfrew, D. T. (2018). Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/17M1143125","ieee":"L. Erdös, T. H. Krüger, and D. T. Renfrew, “Power law decay for systems of randomly coupled differential equations,” SIAM Journal on Mathematical Analysis, vol. 50, no. 3. Society for Industrial and Applied Mathematics , pp. 3271–3290, 2018.","ista":"Erdös L, Krüger TH, Renfrew DT. 2018. Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. 50(3), 3271–3290.","ama":"Erdös L, Krüger TH, Renfrew DT. Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. 2018;50(3):3271-3290. doi:10.1137/17M1143125"},"page":"3271 - 3290","day":"01","article_processing_charge":"No","scopus_import":"1","oa_version":"Published Version","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"181","title":"Power law decay for systems of randomly coupled differential equations","status":"public","intvolume":" 50","abstract":[{"text":"We consider large random matrices X with centered, independent entries but possibly di erent variances. We compute the normalized trace of f(X)g(X∗) for f, g functions analytic on the spectrum of X. We use these results to compute the long time asymptotics for systems of coupled di erential equations with random coe cients. We show that when the coupling is critical, the norm squared of the solution decays like t−1/2.","lang":"eng"}],"issue":"3","type":"journal_article","doi":"10.1137/17M1143125","language":[{"iso":"eng"}],"external_id":{"arxiv":["1708.01546"],"isi":["000437018500032"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.01546"}],"oa":1,"quality_controlled":"1","isi":1,"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"},{"call_identifier":"FWF","name":"Structured Non-Hermitian Random Matrices","_id":"258F40A4-B435-11E9-9278-68D0E5697425","grant_number":"M02080"}],"month":"01","author":[{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"last_name":"Krüger","first_name":"Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H"},{"orcid":"0000-0003-3493-121X","id":"4845BF6A-F248-11E8-B48F-1D18A9856A87","last_name":"Renfrew","first_name":"David T","full_name":"Renfrew, David T"}],"date_created":"2018-12-11T11:45:03Z","date_updated":"2023-09-15T12:05:52Z","volume":50,"year":"2018","acknowledgement":"The work of the second author was also partially supported by the Hausdorff Center of Mathematics.","publication_status":"published","publisher":"Society for Industrial and Applied Mathematics ","department":[{"_id":"LaEr"}],"publist_id":"7740","ec_funded":1},{"oa_version":"Preprint","status":"public","title":"Bounds on the norm of Wigner-type random matrices","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"5971","abstract":[{"lang":"eng","text":"We consider a Wigner-type ensemble, i.e. large hermitian N×N random matrices H=H∗ with centered independent entries and with a general matrix of variances Sxy=𝔼∣∣Hxy∣∣2. The norm of H is asymptotically given by the maximum of the support of the self-consistent density of states. We establish a bound on this maximum in terms of norms of powers of S that substantially improves the earlier bound 2∥S∥1/2∞ given in [O. Ajanki, L. Erdős and T. Krüger, Universality for general Wigner-type matrices, Prob. Theor. Rel. Fields169 (2017) 667–727]. The key element of the proof is an effective Markov chain approximation for the contributions of the weighted Dyck paths appearing in the iterative solution of the corresponding Dyson equation."}],"type":"journal_article","date_published":"2018-09-26T00:00:00Z","citation":{"ama":"Erdös L, Mühlbacher P. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications. 2018. doi:10.1142/s2010326319500096","ista":"Erdös L, Mühlbacher P. 2018. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications., 1950009.","apa":"Erdös, L., & Mühlbacher, P. (2018). Bounds on the norm of Wigner-type random matrices. Random Matrices: Theory and Applications. World Scientific Publishing. https://doi.org/10.1142/s2010326319500096","ieee":"L. Erdös and P. Mühlbacher, “Bounds on the norm of Wigner-type random matrices,” Random matrices: Theory and applications. World Scientific Publishing, 2018.","mla":"Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random Matrices.” Random Matrices: Theory and Applications, 1950009, World Scientific Publishing, 2018, doi:10.1142/s2010326319500096.","short":"L. Erdös, P. Mühlbacher, Random Matrices: Theory and Applications (2018).","chicago":"Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random Matrices.” Random Matrices: Theory and Applications. World Scientific Publishing, 2018. https://doi.org/10.1142/s2010326319500096."},"publication":"Random matrices: Theory and applications","article_processing_charge":"No","day":"26","scopus_import":"1","date_created":"2019-02-13T10:40:54Z","date_updated":"2023-09-19T14:24:05Z","author":[{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"first_name":"Peter","last_name":"Mühlbacher","full_name":"Mühlbacher, Peter"}],"department":[{"_id":"LaEr"}],"publisher":"World Scientific Publishing","publication_status":"published","year":"2018","ec_funded":1,"article_number":"1950009","language":[{"iso":"eng"}],"doi":"10.1142/s2010326319500096","project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"isi":1,"quality_controlled":"1","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1802.05175","open_access":"1"}],"external_id":{"isi":["000477677200002"],"arxiv":["1802.05175"]},"publication_identifier":{"issn":["2010-3263"],"eissn":["2010-3271"]},"month":"09"},{"author":[{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","first_name":"Dominik J"}],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"6179"}]},"date_created":"2018-12-11T11:49:41Z","date_updated":"2023-09-22T09:44:21Z","volume":2018,"year":"2018","publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Oxford University Press","ec_funded":1,"publist_id":"6383","doi":"10.1093/imrn/rnw330","language":[{"iso":"eng"}],"oa":1,"external_id":{"arxiv":["1608.05163"],"isi":["000441668300009"]},"main_file_link":[{"url":"https://arxiv.org/abs/1608.05163","open_access":"1"}],"isi":1,"quality_controlled":"1","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"}],"month":"05","publication_identifier":{"issn":["10737928"]},"oa_version":"Preprint","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"1012","status":"public","title":"Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues","intvolume":" 2018","abstract":[{"lang":"eng","text":"We prove a new central limit theorem (CLT) for the difference of linear eigenvalue statistics of a Wigner random matrix H and its minor H and find that the fluctuation is much smaller than the fluctuations of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of H and H. In particular, our theorem identifies the fluctuation of Kerov's rectangular Young diagrams, defined by the interlacing eigenvalues ofH and H, around their asymptotic shape, the Vershik'Kerov'Logan'Shepp curve. Young diagrams equipped with the Plancherel measure follow the same limiting shape. For this, algebraically motivated, ensemble a CLT has been obtained in Ivanov and Olshanski [20] which is structurally similar to our result but the variance is different, indicating that the analogy between the two models has its limitations. Moreover, our theorem shows that Borodin's result [7] on the convergence of the spectral distribution of Wigner matrices to a Gaussian free field also holds in derivative sense."}],"issue":"10","type":"journal_article","date_published":"2018-05-18T00:00:00Z","publication":"International Mathematics Research Notices","citation":{"mla":"Erdös, László, and Dominik J. Schröder. “Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues.” International Mathematics Research Notices, vol. 2018, no. 10, Oxford University Press, 2018, pp. 3255–98, doi:10.1093/imrn/rnw330.","short":"L. Erdös, D.J. Schröder, International Mathematics Research Notices 2018 (2018) 3255–3298.","chicago":"Erdös, László, and Dominik J Schröder. “Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues.” International Mathematics Research Notices. Oxford University Press, 2018. https://doi.org/10.1093/imrn/rnw330.","ama":"Erdös L, Schröder DJ. Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. 2018;2018(10):3255-3298. doi:10.1093/imrn/rnw330","ista":"Erdös L, Schröder DJ. 2018. Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. 2018(10), 3255–3298.","apa":"Erdös, L., & Schröder, D. J. (2018). Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnw330","ieee":"L. Erdös and D. J. Schröder, “Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues,” International Mathematics Research Notices, vol. 2018, no. 10. Oxford University Press, pp. 3255–3298, 2018."},"page":"3255-3298","day":"18","article_processing_charge":"No","scopus_import":"1"},{"publication_status":"published","publisher":"Instituto Nacional de Matematica Pura e Aplicada","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"year":"2018","date_updated":"2023-10-10T13:11:29Z","date_created":"2018-12-11T11:44:28Z","volume":15,"author":[{"full_name":"Nejjar, Peter","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","first_name":"Peter","last_name":"Nejjar"}],"file_date_updated":"2020-07-14T12:47:46Z","ec_funded":1,"quality_controlled":"1","isi":1,"project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"},{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"}],"oa":1,"external_id":{"isi":["000460475800022"],"arxiv":["1705.08836"]},"language":[{"iso":"eng"}],"doi":"10.30757/ALEA.v15-49","month":"10","publication_identifier":{"issn":["1980-0436"]},"ddc":["510"],"title":"Transition to shocks in TASEP and decoupling of last passage times","status":"public","intvolume":" 15","_id":"70","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","file":[{"file_name":"2018_ALEA_Nejjar.pdf","access_level":"open_access","creator":"kschuh","content_type":"application/pdf","file_size":394851,"file_id":"5981","relation":"main_file","date_updated":"2020-07-14T12:47:46Z","date_created":"2019-02-14T09:44:10Z","checksum":"2ded46aa284a836a8cbb34133a64f1cb"}],"type":"journal_article","abstract":[{"lang":"eng","text":"We consider the totally asymmetric simple exclusion process in a critical scaling parametrized by a≥0, which creates a shock in the particle density of order aT−1/3, T the observation time. When starting from step initial data, we provide bounds on the limiting law which in particular imply that in the double limit lima→∞limT→∞ one recovers the product limit law and the degeneration of the correlation length observed at shocks of order 1. This result is shown to apply to a general last-passage percolation model. We also obtain bounds on the two-point functions of several airy processes."}],"issue":"2","article_type":"original","page":"1311-1334","publication":"Latin American Journal of Probability and Mathematical Statistics","citation":{"ama":"Nejjar P. Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. 2018;15(2):1311-1334. doi:10.30757/ALEA.v15-49","ista":"Nejjar P. 2018. Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. 15(2), 1311–1334.","ieee":"P. Nejjar, “Transition to shocks in TASEP and decoupling of last passage times,” Latin American Journal of Probability and Mathematical Statistics, vol. 15, no. 2. Instituto Nacional de Matematica Pura e Aplicada, pp. 1311–1334, 2018.","apa":"Nejjar, P. (2018). Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. Instituto Nacional de Matematica Pura e Aplicada. https://doi.org/10.30757/ALEA.v15-49","mla":"Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” Latin American Journal of Probability and Mathematical Statistics, vol. 15, no. 2, Instituto Nacional de Matematica Pura e Aplicada, 2018, pp. 1311–34, doi:10.30757/ALEA.v15-49.","short":"P. Nejjar, Latin American Journal of Probability and Mathematical Statistics 15 (2018) 1311–1334.","chicago":"Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” Latin American Journal of Probability and Mathematical Statistics. Instituto Nacional de Matematica Pura e Aplicada, 2018. https://doi.org/10.30757/ALEA.v15-49."},"date_published":"2018-10-01T00:00:00Z","scopus_import":"1","day":"01","has_accepted_license":"1","article_processing_charge":"No"},{"author":[{"orcid":"0000-0003-1109-5511","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","last_name":"Virosztek","first_name":"Daniel","full_name":"Virosztek, Daniel"}],"volume":84,"date_updated":"2023-10-16T10:29:22Z","date_created":"2018-12-11T11:45:36Z","acknowledgement":"The author was supported by the ISTFELLOW program of the Institute of Science and Technol- ogy Austria (project code IC1027FELL01) and partially supported by the Hungarian National Research, Development and Innovation Office, NKFIH (grant no. K124152).","year":"2018","publisher":"Springer Nature","department":[{"_id":"LaEr"}],"publication_status":"published","ec_funded":1,"publist_id":"7615","doi":"10.14232/actasm-018-753-y","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1802.03305"}],"external_id":{"arxiv":["1802.03305"]},"project":[{"call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","publication_identifier":{"eissn":["2064-8316"],"issn":["0001-6969"]},"month":"06","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"284","intvolume":" 84","title":"Maps on probability measures preserving certain distances - a survey and some new results","status":"public","issue":"1-2","abstract":[{"text":"Borel probability measures living on metric spaces are fundamental\r\nmathematical objects. There are several meaningful distance functions that make the collection of the probability measures living on a certain space a metric space. We are interested in the description of the structure of the isometries of such metric spaces. We overview some of the recent results of the topic and we also provide some new ones concerning the Wasserstein distance. More specifically, we consider the space of all Borel probability measures on the unit sphere of a Euclidean space endowed with the Wasserstein metric W_p for arbitrary p >= 1, and we show that the action of a Wasserstein isometry on the set of Dirac measures is induced by an isometry of the underlying unit sphere.","lang":"eng"}],"type":"journal_article","date_published":"2018-06-04T00:00:00Z","citation":{"chicago":"Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances - a Survey and Some New Results.” Acta Scientiarum Mathematicarum. Springer Nature, 2018. https://doi.org/10.14232/actasm-018-753-y.","short":"D. Virosztek, Acta Scientiarum Mathematicarum 84 (2018) 65–80.","mla":"Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances - a Survey and Some New Results.” Acta Scientiarum Mathematicarum, vol. 84, no. 1–2, Springer Nature, 2018, pp. 65–80, doi:10.14232/actasm-018-753-y.","ieee":"D. Virosztek, “Maps on probability measures preserving certain distances - a survey and some new results,” Acta Scientiarum Mathematicarum, vol. 84, no. 1–2. Springer Nature, pp. 65–80, 2018.","apa":"Virosztek, D. (2018). Maps on probability measures preserving certain distances - a survey and some new results. Acta Scientiarum Mathematicarum. Springer Nature. https://doi.org/10.14232/actasm-018-753-y","ista":"Virosztek D. 2018. Maps on probability measures preserving certain distances - a survey and some new results. Acta Scientiarum Mathematicarum. 84(1–2), 65–80.","ama":"Virosztek D. Maps on probability measures preserving certain distances - a survey and some new results. Acta Scientiarum Mathematicarum. 2018;84(1-2):65-80. doi:10.14232/actasm-018-753-y"},"publication":"Acta Scientiarum Mathematicarum","page":"65 - 80","article_type":"original","article_processing_charge":"No","day":"04","scopus_import":"1"},{"publication":"arXiv","oa":1,"citation":{"ista":"Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. arXiv, 1804.07752.","apa":"Alt, J., Erdös, L., & Krüger, T. H. (n.d.). The Dyson equation with linear self-energy: Spectral bands, edges and cusps. arXiv.","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy: Spectral bands, edges and cusps,” arXiv. .","ama":"Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. arXiv.","chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” ArXiv, n.d.","mla":"Alt, Johannes, et al. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” ArXiv, 1804.07752.","short":"J. Alt, L. Erdös, T.H. Krüger, ArXiv (n.d.)."},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.07752"}],"external_id":{"arxiv":["1804.07752"]},"date_published":"2018-04-20T00:00:00Z","language":[{"iso":"eng"}],"day":"20","month":"04","article_processing_charge":"No","_id":"6183","year":"2018","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"The Dyson equation with linear self-energy: Spectral bands, edges and cusps","status":"public","publication_status":"submitted","department":[{"_id":"LaEr"}],"author":[{"id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","first_name":"Johannes","last_name":"Alt","full_name":"Alt, Johannes"},{"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","last_name":"Krüger","first_name":"Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87"}],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"149"},{"id":"14694","status":"public","relation":"later_version"}]},"date_created":"2019-03-28T09:20:06Z","date_updated":"2023-12-18T10:46:08Z","oa_version":"Preprint","article_number":"1804.07752","type":"preprint","abstract":[{"text":"We study the unique solution $m$ of the Dyson equation \\[ -m(z)^{-1} = z - a\r\n+ S[m(z)] \\] on a von Neumann algebra $\\mathcal{A}$ with the constraint\r\n$\\mathrm{Im}\\,m\\geq 0$. Here, $z$ lies in the complex upper half-plane, $a$ is\r\na self-adjoint element of $\\mathcal{A}$ and $S$ is a positivity-preserving\r\nlinear operator on $\\mathcal{A}$. We show that $m$ is the Stieltjes transform\r\nof a compactly supported $\\mathcal{A}$-valued measure on $\\mathbb{R}$. Under\r\nsuitable assumptions, we establish that this measure has a uniformly\r\n$1/3$-H\\\"{o}lder continuous density with respect to the Lebesgue measure, which\r\nis supported on finitely many intervals, called bands. In fact, the density is\r\nanalytic inside the bands with a square-root growth at the edges and internal\r\ncubic root cusps whenever the gap between two bands vanishes. The shape of\r\nthese singularities is universal and no other singularity may occur. We give a\r\nprecise asymptotic description of $m$ near the singular points. These\r\nasymptotics generalize the analysis at the regular edges given in the companion\r\npaper on the Tracy-Widom universality for the edge eigenvalue statistics for\r\ncorrelated random matrices [arXiv:1804.07744] and they play a key role in the\r\nproof of the Pearcey universality at the cusp for Wigner-type matrices\r\n[arXiv:1809.03971,arXiv:1811.04055]. We also extend the finite dimensional band\r\nmass formula from [arXiv:1804.07744] to the von Neumann algebra setting by\r\nshowing that the spectral mass of the bands is topologically rigid under\r\ndeformations and we conclude that these masses are quantized in some important\r\ncases.","lang":"eng"}]},{"year":"2018","publication_status":"published","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"publisher":"Springer Nature","author":[{"last_name":"Betea","first_name":"Dan","full_name":"Betea, Dan"},{"full_name":"Bouttier, Jeremie","last_name":"Bouttier","first_name":"Jeremie"},{"id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","last_name":"Nejjar","first_name":"Peter","full_name":"Nejjar, Peter"},{"full_name":"Vuletic, Mirjana","last_name":"Vuletic","first_name":"Mirjana"}],"date_created":"2018-12-11T11:47:09Z","date_updated":"2024-02-20T10:48:17Z","volume":19,"file_date_updated":"2020-07-14T12:47:03Z","ec_funded":1,"publist_id":"7258","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":["1704.05809"]},"oa":1,"quality_controlled":"1","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"}],"doi":"10.1007/s00023-018-0723-1","language":[{"iso":"eng"}],"month":"11","publication_identifier":{"issn":["1424-0637"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"556","ddc":["500"],"title":"The free boundary Schur process and applications I","status":"public","intvolume":" 19","file":[{"access_level":"open_access","file_name":"2018_Annales_Betea.pdf","file_size":3084674,"content_type":"application/pdf","creator":"dernst","relation":"main_file","file_id":"5866","checksum":"0c38abe73569b7166b7487ad5d23cc68","date_created":"2019-01-21T15:18:55Z","date_updated":"2020-07-14T12:47:03Z"}],"oa_version":"Published Version","type":"journal_article","abstract":[{"lang":"eng","text":"We investigate the free boundary Schur process, a variant of the Schur process introduced by Okounkov and Reshetikhin, where we allow the first and the last partitions to be arbitrary (instead of empty in the original setting). The pfaffian Schur process, previously studied by several authors, is recovered when just one of the boundary partitions is left free. We compute the correlation functions of the process in all generality via the free fermion formalism, which we extend with the thorough treatment of “free boundary states.” For the case of one free boundary, our approach yields a new proof that the process is pfaffian. For the case of two free boundaries, we find that the process is not pfaffian, but a closely related process is. We also study three different applications of the Schur process with one free boundary: fluctuations of symmetrized last passage percolation models, limit shapes and processes for symmetric plane partitions and for plane overpartitions."}],"issue":"12","publication":"Annales Henri Poincare","citation":{"short":"D. Betea, J. Bouttier, P. Nejjar, M. Vuletic, Annales Henri Poincare 19 (2018) 3663–3742.","mla":"Betea, Dan, et al. “The Free Boundary Schur Process and Applications I.” Annales Henri Poincare, vol. 19, no. 12, Springer Nature, 2018, pp. 3663–742, doi:10.1007/s00023-018-0723-1.","chicago":"Betea, Dan, Jeremie Bouttier, Peter Nejjar, and Mirjana Vuletic. “The Free Boundary Schur Process and Applications I.” Annales Henri Poincare. Springer Nature, 2018. https://doi.org/10.1007/s00023-018-0723-1.","ama":"Betea D, Bouttier J, Nejjar P, Vuletic M. The free boundary Schur process and applications I. Annales Henri Poincare. 2018;19(12):3663-3742. doi:10.1007/s00023-018-0723-1","ieee":"D. Betea, J. Bouttier, P. Nejjar, and M. Vuletic, “The free boundary Schur process and applications I,” Annales Henri Poincare, vol. 19, no. 12. Springer Nature, pp. 3663–3742, 2018.","apa":"Betea, D., Bouttier, J., Nejjar, P., & Vuletic, M. (2018). The free boundary Schur process and applications I. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-018-0723-1","ista":"Betea D, Bouttier J, Nejjar P, Vuletic M. 2018. The free boundary Schur process and applications I. Annales Henri Poincare. 19(12), 3663–3742."},"article_type":"original","page":"3663-3742","date_published":"2018-11-13T00:00:00Z","scopus_import":"1","day":"13","has_accepted_license":"1","article_processing_charge":"Yes (via OA deal)"},{"publist_id":"7772","ec_funded":1,"file_date_updated":"2020-07-14T12:44:57Z","department":[{"_id":"LaEr"}],"publisher":"Institute of Science and Technology Austria","publication_status":"published","year":"2018","date_created":"2018-12-11T11:44:53Z","date_updated":"2024-02-22T14:34:33Z","related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"1677"},{"id":"550","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"6183"},{"relation":"part_of_dissertation","status":"public","id":"566"},{"id":"1010","status":"public","relation":"part_of_dissertation"},{"id":"6240","relation":"part_of_dissertation","status":"public"},{"id":"6184","relation":"part_of_dissertation","status":"public"}]},"author":[{"first_name":"Johannes","last_name":"Alt","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","full_name":"Alt, Johannes"}],"publication_identifier":{"issn":["2663-337X"]},"month":"07","project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"}],"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,"language":[{"iso":"eng"}],"supervisor":[{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"}],"degree_awarded":"PhD","doi":"10.15479/AT:ISTA:TH_1040","alternative_title":["ISTA Thesis"],"type":"dissertation","abstract":[{"lang":"eng","text":"The eigenvalue density of many large random matrices is well approximated by a deterministic measure, the self-consistent density of states. In the present work, we show this behaviour for several classes of random matrices. In fact, we establish that, in each of these classes, the self-consistent density of states approximates the eigenvalue density of the random matrix on all scales slightly above the typical eigenvalue spacing. For large classes of random matrices, the self-consistent density of states exhibits several universal features. We prove that, under suitable assumptions, random Gram matrices and Hermitian random matrices with decaying correlations have a 1/3-Hölder continuous self-consistent density of states ρ on R, which is analytic, where it is positive, and has either a square root edge or a cubic root cusp, where it vanishes. We, thus, extend the validity of the corresponding result for Wigner-type matrices from [4, 5, 7]. We show that ρ is determined as the inverse Stieltjes transform of the normalized trace of the unique solution m(z) to the Dyson equation −m(z) −1 = z − a + S[m(z)] on C N×N with the constraint Im m(z) ≥ 0. Here, z lies in the complex upper half-plane, a is a self-adjoint element of C N×N and S is a positivity-preserving operator on C N×N encoding the first two moments of the random matrix. In order to analyze a possible limit of ρ for N → ∞ and address some applications in free probability theory, we also consider the Dyson equation on infinite dimensional von Neumann algebras. We present two applications to random matrices. We first establish that, under certain assumptions, large random matrices with independent entries have a rotationally symmetric self-consistent density of states which is supported on a centered disk in C. Moreover, it is infinitely often differentiable apart from a jump on the boundary of this disk. Second, we show edge universality at all regular (not necessarily extreme) spectral edges for Hermitian random matrices with decaying correlations."}],"title":"Dyson equation and eigenvalue statistics of random matrices","status":"public","ddc":["515","519"],"_id":"149","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","file":[{"date_created":"2019-04-08T13:55:20Z","date_updated":"2020-07-14T12:44:57Z","checksum":"d4dad55a7513f345706aaaba90cb1bb8","relation":"main_file","file_id":"6241","file_size":5801709,"content_type":"application/pdf","creator":"dernst","file_name":"2018_thesis_Alt.pdf","access_level":"open_access"},{"creator":"dernst","file_size":3802059,"content_type":"application/zip","access_level":"closed","file_name":"2018_thesis_Alt_source.zip","checksum":"d73fcf46300dce74c403f2b491148ab4","date_created":"2019-04-08T13:55:20Z","date_updated":"2020-07-14T12:44:57Z","file_id":"6242","relation":"source_file"}],"oa_version":"Published Version","pubrep_id":"1040","has_accepted_license":"1","article_processing_charge":"No","day":"12","page":"456","citation":{"ama":"Alt J. Dyson equation and eigenvalue statistics of random matrices. 2018. doi:10.15479/AT:ISTA:TH_1040","ista":"Alt J. 2018. Dyson equation and eigenvalue statistics of random matrices. Institute of Science and Technology Austria.","ieee":"J. Alt, “Dyson equation and eigenvalue statistics of random matrices,” Institute of Science and Technology Austria, 2018.","apa":"Alt, J. (2018). Dyson equation and eigenvalue statistics of random matrices. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:TH_1040","mla":"Alt, Johannes. Dyson Equation and Eigenvalue Statistics of Random Matrices. Institute of Science and Technology Austria, 2018, doi:10.15479/AT:ISTA:TH_1040.","short":"J. Alt, Dyson Equation and Eigenvalue Statistics of Random Matrices, Institute of Science and Technology Austria, 2018.","chicago":"Alt, Johannes. “Dyson Equation and Eigenvalue Statistics of Random Matrices.” Institute of Science and Technology Austria, 2018. https://doi.org/10.15479/AT:ISTA:TH_1040."},"date_published":"2018-07-12T00:00:00Z"},{"day":"25","scopus_import":1,"date_published":"2017-08-25T00:00:00Z","publication":"Advances in Theoretical and Mathematical Physics","citation":{"ama":"Bourgade P, Erdös L, Yau H, Yin J. Universality for a class of random band matrices. Advances in Theoretical and Mathematical Physics. 2017;21(3):739-800. doi:10.4310/ATMP.2017.v21.n3.a5","ista":"Bourgade P, Erdös L, Yau H, Yin J. 2017. Universality for a class of random band matrices. Advances in Theoretical and Mathematical Physics. 21(3), 739–800.","apa":"Bourgade, P., Erdös, L., Yau, H., & Yin, J. (2017). Universality for a class of random band matrices. Advances in Theoretical and Mathematical Physics. International Press. https://doi.org/10.4310/ATMP.2017.v21.n3.a5","ieee":"P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Universality for a class of random band matrices,” Advances in Theoretical and Mathematical Physics, vol. 21, no. 3. International Press, pp. 739–800, 2017.","mla":"Bourgade, Paul, et al. “Universality for a Class of Random Band Matrices.” Advances in Theoretical and Mathematical Physics, vol. 21, no. 3, International Press, 2017, pp. 739–800, doi:10.4310/ATMP.2017.v21.n3.a5.","short":"P. Bourgade, L. Erdös, H. Yau, J. Yin, Advances in Theoretical and Mathematical Physics 21 (2017) 739–800.","chicago":"Bourgade, Paul, László Erdös, Horng Yau, and Jun Yin. “Universality for a Class of Random Band Matrices.” Advances in Theoretical and Mathematical Physics. International Press, 2017. https://doi.org/10.4310/ATMP.2017.v21.n3.a5."},"page":"739 - 800","abstract":[{"text":"We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, W ~ N. All previous results concerning universality of non-Gaussian random matrices are for mean-field models. By relying on a new mean-field reduction technique, we deduce universality from quantum unique ergodicity for band matrices.","lang":"eng"}],"issue":"3","type":"journal_article","oa_version":"Submitted Version","_id":"483","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Universality for a class of random band matrices","status":"public","intvolume":" 21","month":"08","publication_identifier":{"issn":["10950761"]},"doi":"10.4310/ATMP.2017.v21.n3.a5","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1602.02312"}],"oa":1,"quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"ec_funded":1,"publist_id":"7337","author":[{"full_name":"Bourgade, Paul","last_name":"Bourgade","first_name":"Paul"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"Erdös, László"},{"full_name":"Yau, Horng","last_name":"Yau","first_name":"Horng"},{"full_name":"Yin, Jun","first_name":"Jun","last_name":"Yin"}],"date_created":"2018-12-11T11:46:43Z","date_updated":"2021-01-12T08:00:57Z","volume":21,"year":"2017","publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"International Press"},{"ec_funded":1,"publist_id":"7247","date_created":"2018-12-11T11:47:13Z","date_updated":"2022-05-24T06:57:28Z","volume":28,"author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"Erdös, László"},{"full_name":"Yau, Horng","last_name":"Yau","first_name":"Horng"}],"publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"American Mathematical Society","year":"2017","month":"01","publication_identifier":{"eisbn":["978-1-4704-4194-4"],"isbn":["9-781-4704-3648-3"]},"language":[{"iso":"eng"}],"doi":"10.1090/cln/028","quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"abstract":[{"lang":"eng","text":"This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality.\r\n"}],"alternative_title":["Courant Lecture Notes"],"type":"book","oa_version":"None","title":"A Dynamical Approach to Random Matrix Theory","status":"public","intvolume":" 28","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"567","day":"01","article_processing_charge":"No","series_title":"Courant Lecture Notes","date_published":"2017-01-01T00:00:00Z","page":"226","citation":{"mla":"Erdös, László, and Horng Yau. A Dynamical Approach to Random Matrix Theory. Vol. 28, American Mathematical Society, 2017, doi:10.1090/cln/028.","short":"L. Erdös, H. Yau, A Dynamical Approach to Random Matrix Theory, American Mathematical Society, 2017.","chicago":"Erdös, László, and Horng Yau. A Dynamical Approach to Random Matrix Theory. Vol. 28. Courant Lecture Notes. American Mathematical Society, 2017. https://doi.org/10.1090/cln/028.","ama":"Erdös L, Yau H. A Dynamical Approach to Random Matrix Theory. Vol 28. American Mathematical Society; 2017. doi:10.1090/cln/028","ista":"Erdös L, Yau H. 2017. A Dynamical Approach to Random Matrix Theory, American Mathematical Society, 226p.","apa":"Erdös, L., & Yau, H. (2017). A Dynamical Approach to Random Matrix Theory (Vol. 28). American Mathematical Society. https://doi.org/10.1090/cln/028","ieee":"L. Erdös and H. Yau, A Dynamical Approach to Random Matrix Theory, vol. 28. American Mathematical Society, 2017."}},{"publist_id":"7189","ec_funded":1,"publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","year":"2017","date_updated":"2021-01-12T08:06:22Z","date_created":"2018-12-11T11:47:30Z","volume":53,"author":[{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0954-3231","first_name":"Kevin","last_name":"Schnelli","full_name":"Schnelli, Kevin"}],"month":"11","publication_identifier":{"issn":["02460203"]},"quality_controlled":"1","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"main_file_link":[{"url":"https://arxiv.org/abs/1504.00650","open_access":"1"}],"oa":1,"language":[{"iso":"eng"}],"doi":"10.1214/16-AIHP765","type":"journal_article","abstract":[{"lang":"eng","text":"We show that the Dyson Brownian Motion exhibits local universality after a very short time assuming that local rigidity and level repulsion of the eigenvalues hold. These conditions are verified, hence bulk spectral universality is proven, for a large class of Wigner-like matrices, including deformed Wigner ensembles and ensembles with non-stochastic variance matrices whose limiting densities differ from Wigner's semicircle law."}],"issue":"4","status":"public","title":"Universality for random matrix flows with time dependent density","intvolume":" 53","_id":"615","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","oa_version":"Submitted Version","scopus_import":1,"day":"01","page":"1606 - 1656","publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","citation":{"chicago":"Erdös, László, and Kevin Schnelli. “Universality for Random Matrix Flows with Time Dependent Density.” Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/16-AIHP765.","mla":"Erdös, László, and Kevin Schnelli. “Universality for Random Matrix Flows with Time Dependent Density.” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 53, no. 4, Institute of Mathematical Statistics, 2017, pp. 1606–56, doi:10.1214/16-AIHP765.","short":"L. Erdös, K. Schnelli, Annales de l’institut Henri Poincare (B) Probability and Statistics 53 (2017) 1606–1656.","ista":"Erdös L, Schnelli K. 2017. Universality for random matrix flows with time dependent density. Annales de l’institut Henri Poincare (B) Probability and Statistics. 53(4), 1606–1656.","apa":"Erdös, L., & Schnelli, K. (2017). Universality for random matrix flows with time dependent density. Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/16-AIHP765","ieee":"L. Erdös and K. Schnelli, “Universality for random matrix flows with time dependent density,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 53, no. 4. Institute of Mathematical Statistics, pp. 1606–1656, 2017.","ama":"Erdös L, Schnelli K. Universality for random matrix flows with time dependent density. Annales de l’institut Henri Poincare (B) Probability and Statistics. 2017;53(4):1606-1656. doi:10.1214/16-AIHP765"},"date_published":"2017-11-01T00:00:00Z"},{"ec_funded":1,"publist_id":"6959","author":[{"full_name":"Ajanki, Oskari H","first_name":"Oskari H","last_name":"Ajanki","id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","last_name":"Krüger","first_name":"Torben H","full_name":"Krüger, Torben H"},{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"}],"date_created":"2018-12-11T11:48:08Z","date_updated":"2021-01-12T08:12:24Z","volume":70,"year":"2017","publication_status":"published","department":[{"_id":"LaEr"}],"publisher":"Wiley-Blackwell","month":"09","publication_identifier":{"issn":["00103640"]},"doi":"10.1002/cpa.21639","language":[{"iso":"eng"}],"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1512.03703"}],"quality_controlled":"1","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"abstract":[{"lang":"eng","text":"Let S be a positivity-preserving symmetric linear operator acting on bounded functions. The nonlinear equation -1/m=z+Sm with a parameter z in the complex upper half-plane ℍ has a unique solution m with values in ℍ. We show that the z-dependence of this solution can be represented as the Stieltjes transforms of a family of probability measures v on ℝ. Under suitable conditions on S, we show that v has a real analytic density apart from finitely many algebraic singularities of degree at most 3. Our motivation comes from large random matrices. The solution m determines the density of eigenvalues of two prominent matrix ensembles: (i) matrices with centered independent entries whose variances are given by S and (ii) matrices with correlated entries with a translation-invariant correlation structure. Our analysis shows that the limiting eigenvalue density has only square root singularities or cubic root cusps; no other singularities occur."}],"issue":"9","type":"journal_article","oa_version":"Submitted Version","_id":"721","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","status":"public","title":"Singularities of solutions to quadratic vector equations on the complex upper half plane","intvolume":" 70","day":"01","scopus_import":1,"date_published":"2017-09-01T00:00:00Z","publication":"Communications on Pure and Applied Mathematics","citation":{"chicago":"Ajanki, Oskari H, Torben H Krüger, and László Erdös. “Singularities of Solutions to Quadratic Vector Equations on the Complex Upper Half Plane.” Communications on Pure and Applied Mathematics. Wiley-Blackwell, 2017. https://doi.org/10.1002/cpa.21639.","short":"O.H. Ajanki, T.H. Krüger, L. Erdös, Communications on Pure and Applied Mathematics 70 (2017) 1672–1705.","mla":"Ajanki, Oskari H., et al. “Singularities of Solutions to Quadratic Vector Equations on the Complex Upper Half Plane.” Communications on Pure and Applied Mathematics, vol. 70, no. 9, Wiley-Blackwell, 2017, pp. 1672–705, doi:10.1002/cpa.21639.","apa":"Ajanki, O. H., Krüger, T. H., & Erdös, L. (2017). Singularities of solutions to quadratic vector equations on the complex upper half plane. Communications on Pure and Applied Mathematics. Wiley-Blackwell. https://doi.org/10.1002/cpa.21639","ieee":"O. H. Ajanki, T. H. Krüger, and L. Erdös, “Singularities of solutions to quadratic vector equations on the complex upper half plane,” Communications on Pure and Applied Mathematics, vol. 70, no. 9. Wiley-Blackwell, pp. 1672–1705, 2017.","ista":"Ajanki OH, Krüger TH, Erdös L. 2017. Singularities of solutions to quadratic vector equations on the complex upper half plane. Communications on Pure and Applied Mathematics. 70(9), 1672–1705.","ama":"Ajanki OH, Krüger TH, Erdös L. Singularities of solutions to quadratic vector equations on the complex upper half plane. Communications on Pure and Applied Mathematics. 2017;70(9):1672-1705. doi:10.1002/cpa.21639"},"page":"1672 - 1705"},{"related_material":{"record":[{"id":"149","status":"public","relation":"dissertation_contains"}]},"author":[{"id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","first_name":"Johannes","last_name":"Alt","full_name":"Alt, Johannes"}],"volume":22,"date_updated":"2023-09-07T12:38:08Z","date_created":"2018-12-11T11:47:07Z","year":"2017","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","publication_status":"published","publist_id":"7265","ec_funded":1,"file_date_updated":"2020-07-14T12:47:00Z","article_number":"63","doi":"10.1214/17-ECP97","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"},"oa":1,"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"}],"quality_controlled":"1","publication_identifier":{"issn":["1083589X"]},"month":"11","pubrep_id":"926","oa_version":"Published Version","file":[{"file_size":470876,"content_type":"application/pdf","creator":"system","file_name":"IST-2018-926-v1+1_euclid.ecp.1511233247.pdf","access_level":"open_access","date_updated":"2020-07-14T12:47:00Z","date_created":"2018-12-12T10:08:04Z","checksum":"0ec05303a0de190de145654237984c79","relation":"main_file","file_id":"4663"}],"_id":"550","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":" 22","ddc":["539"],"title":"Singularities of the density of states of random Gram matrices","status":"public","abstract":[{"lang":"eng","text":"For large random matrices X with independent, centered entries but not necessarily identical variances, the eigenvalue density of XX* is well-approximated by a deterministic measure on ℝ. We show that the density of this measure has only square and cubic-root singularities away from zero. We also extend the bulk local law in [5] to the vicinity of these singularities."}],"type":"journal_article","date_published":"2017-11-21T00:00:00Z","citation":{"ama":"Alt J. Singularities of the density of states of random Gram matrices. Electronic Communications in Probability. 2017;22. doi:10.1214/17-ECP97","ieee":"J. Alt, “Singularities of the density of states of random Gram matrices,” Electronic Communications in Probability, vol. 22. Institute of Mathematical Statistics, 2017.","apa":"Alt, J. (2017). Singularities of the density of states of random Gram matrices. Electronic Communications in Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/17-ECP97","ista":"Alt J. 2017. Singularities of the density of states of random Gram matrices. Electronic Communications in Probability. 22, 63.","short":"J. Alt, Electronic Communications in Probability 22 (2017).","mla":"Alt, Johannes. “Singularities of the Density of States of Random Gram Matrices.” Electronic Communications in Probability, vol. 22, 63, Institute of Mathematical Statistics, 2017, doi:10.1214/17-ECP97.","chicago":"Alt, Johannes. “Singularities of the Density of States of Random Gram Matrices.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/17-ECP97."},"publication":"Electronic Communications in Probability","has_accepted_license":"1","day":"21","scopus_import":1},{"author":[{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","first_name":"Dominik J","last_name":"Schröder","full_name":"Schröder, Dominik J"}],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"6179"}]},"date_created":"2018-12-11T11:50:23Z","date_updated":"2023-09-07T12:54:12Z","volume":21,"acknowledgement":"Partially supported by the IST Austria Excellence Scholarship.","year":"2017","publication_status":"published","publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"file_date_updated":"2018-12-12T10:18:10Z","ec_funded":1,"publist_id":"6214","article_number":"86","doi":"10.1214/16-ECP38","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"},"oa":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"}],"month":"01","pubrep_id":"747","oa_version":"Published Version","file":[{"relation":"main_file","file_id":"5329","date_updated":"2018-12-12T10:18:10Z","date_created":"2018-12-12T10:18:10Z","access_level":"open_access","file_name":"IST-2017-747-v1+1_euclid.ecp.1483347665.pdf","file_size":440770,"content_type":"application/pdf","creator":"system"}],"_id":"1144","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","ddc":["510"],"title":"Fluctuations of functions of Wigner matrices","intvolume":" 21","abstract":[{"text":"We show that matrix elements of functions of N × N Wigner matrices fluctuate on a scale of order N−1/2 and we identify the limiting fluctuation. Our result holds for any function f of the matrix that has bounded variation thus considerably relaxing the regularity requirement imposed in [7, 11].","lang":"eng"}],"type":"journal_article","date_published":"2017-01-02T00:00:00Z","publication":"Electronic Communications in Probability","citation":{"chicago":"Erdös, László, and Dominik J Schröder. “Fluctuations of Functions of Wigner Matrices.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/16-ECP38.","short":"L. Erdös, D.J. Schröder, Electronic Communications in Probability 21 (2017).","mla":"Erdös, László, and Dominik J. Schröder. “Fluctuations of Functions of Wigner Matrices.” Electronic Communications in Probability, vol. 21, 86, Institute of Mathematical Statistics, 2017, doi:10.1214/16-ECP38.","ieee":"L. Erdös and D. J. Schröder, “Fluctuations of functions of Wigner matrices,” Electronic Communications in Probability, vol. 21. Institute of Mathematical Statistics, 2017.","apa":"Erdös, L., & Schröder, D. J. (2017). Fluctuations of functions of Wigner matrices. Electronic Communications in Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/16-ECP38","ista":"Erdös L, Schröder DJ. 2017. Fluctuations of functions of Wigner matrices. Electronic Communications in Probability. 21, 86.","ama":"Erdös L, Schröder DJ. Fluctuations of functions of Wigner matrices. Electronic Communications in Probability. 2017;21. doi:10.1214/16-ECP38"},"day":"02","has_accepted_license":"1","scopus_import":1},{"language":[{"iso":"eng"}],"doi":"10.1007/s00440-015-0692-y","isi":1,"quality_controlled":"1","project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"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":{"isi":["000398842700004"]},"month":"04","publication_identifier":{"issn":["01788051"]},"date_updated":"2023-09-20T09:42:12Z","date_created":"2018-12-11T11:52:32Z","volume":167,"author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3036-1475","first_name":"Zhigang","last_name":"Bao","full_name":"Bao, Zhigang"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"}],"publication_status":"published","publisher":"Springer","department":[{"_id":"LaEr"}],"year":"2017","acknowledgement":"Z. Bao was supported by ERC Advanced Grant RANMAT No. 338804; L. Erdős was partially supported by ERC Advanced Grant RANMAT No. 338804.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria). The authors are very grateful to the anonymous referees for careful reading and valuable comments, which helped to improve the organization.","file_date_updated":"2020-07-14T12:45:00Z","ec_funded":1,"publist_id":"5644","date_published":"2017-04-01T00:00:00Z","article_type":"original","page":"673 - 776","publication":"Probability Theory and Related Fields","citation":{"apa":"Bao, Z., & Erdös, L. (2017). Delocalization for a class of random block band matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-015-0692-y","ieee":"Z. Bao and L. Erdös, “Delocalization for a class of random block band matrices,” Probability Theory and Related Fields, vol. 167, no. 3–4. Springer, pp. 673–776, 2017.","ista":"Bao Z, Erdös L. 2017. Delocalization for a class of random block band matrices. Probability Theory and Related Fields. 167(3–4), 673–776.","ama":"Bao Z, Erdös L. Delocalization for a class of random block band matrices. Probability Theory and Related Fields. 2017;167(3-4):673-776. doi:10.1007/s00440-015-0692-y","chicago":"Bao, Zhigang, and László Erdös. “Delocalization for a Class of Random Block Band Matrices.” Probability Theory and Related Fields. Springer, 2017. https://doi.org/10.1007/s00440-015-0692-y.","short":"Z. Bao, L. Erdös, Probability Theory and Related Fields 167 (2017) 673–776.","mla":"Bao, Zhigang, and László Erdös. “Delocalization for a Class of Random Block Band Matrices.” Probability Theory and Related Fields, vol. 167, no. 3–4, Springer, 2017, pp. 673–776, doi:10.1007/s00440-015-0692-y."},"day":"01","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","scopus_import":"1","oa_version":"Published Version","file":[{"file_name":"IST-2016-489-v1+1_s00440-015-0692-y.pdf","access_level":"open_access","file_size":1615755,"content_type":"application/pdf","creator":"system","relation":"main_file","file_id":"4665","date_updated":"2020-07-14T12:45:00Z","date_created":"2018-12-12T10:08:05Z","checksum":"67afa85ff1e220cbc1f9f477a828513c"}],"pubrep_id":"489","title":"Delocalization for a class of random block band matrices","ddc":["530"],"status":"public","intvolume":" 167","_id":"1528","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","abstract":[{"lang":"eng","text":"We consider N×N Hermitian random matrices H consisting of blocks of size M≥N6/7. The matrix elements are i.i.d. within the blocks, close to a Gaussian in the four moment matching sense, but their distribution varies from block to block to form a block-band structure, with an essential band width M. We show that the entries of the Green’s function G(z)=(H−z)−1 satisfy the local semicircle law with spectral parameter z=E+iη down to the real axis for any η≫N−1, using a combination of the supersymmetry method inspired by Shcherbina (J Stat Phys 155(3): 466–499, 2014) and the Green’s function comparison strategy. Previous estimates were valid only for η≫M−1. The new estimate also implies that the eigenvectors in the middle of the spectrum are fully delocalized."}],"issue":"3-4","type":"journal_article"}]