Kyoto RIMS Kôkyûroku, vol. 2125, Research Institute for Mathematical Sciences, Kyoto University, 2019, 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.","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.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"30","volume":2125,"quality_controlled":"1","date_updated":"2021-01-12T08:11:33Z","main_file_link":[{"url":"http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/2125.html","open_access":"1"}],"title":"Dirac masses and isometric rigidity","year":"2019","publication":"Kyoto RIMS Kôkyûroku","type":"conference","oa":1,"_id":"7035","publisher":"Research Institute for Mathematical Sciences, Kyoto University","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"}],"article_processing_charge":"No","intvolume":" 2125","date_created":"2019-11-18T15:39:53Z","language":[{"iso":"eng"}],"conference":{"location":"Kyoto, Japan","name":"Research on isometries as preserver problems and related topics","start_date":"2019-01-28","end_date":"2019-01-30"},"department":[{"_id":"LaEr"}],"page":"34-41","month":"01","oa_version":"Submitted Version"},{"scopus_import":1,"volume":576,"date_published":"2019-09-01T00:00:00Z","ec_funded":1,"publication_status":"published","status":"public","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)","doi":"10.1016/j.laa.2018.03.002","oa_version":"Preprint","month":"09","department":[{"_id":"LaEr"}],"publist_id":"7424","article_processing_charge":"No","_id":"405","abstract":[{"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.","lang":"eng"}],"oa":1,"article_type":"original","project":[{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"publication":"Linear Algebra and Its Applications","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1712.05324"}],"title":"Jointly convex quantum Jensen divergences","year":"2019","quality_controlled":"1","date_updated":"2021-01-12T07:54:08Z","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","day":"01","external_id":{"arxiv":["1712.05324"]},"citation":{"ista":"Virosztek D. 2019. Jointly convex quantum Jensen divergences. Linear Algebra and Its Applications. 576, 67–78.","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.","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","short":"D. Virosztek, Linear Algebra and Its Applications 576 (2019) 67–78.","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","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.","ieee":"D. Virosztek, “Jointly convex quantum Jensen divergences,” *Linear Algebra and Its Applications*, vol. 576. Elsevier, pp. 67–78, 2019."},"author":[{"orcid":"0000-0003-1109-5511","first_name":"Daniel","full_name":"Virosztek, Daniel","last_name":"Virosztek","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"page":"67-78","language":[{"iso":"eng"}],"date_created":"2018-12-11T11:46:17Z","intvolume":" 576","publisher":"Elsevier","type":"journal_article"},{"oa_version":"Published Version","month":"02","file":[{"content_type":"application/pdf","date_created":"2018-12-17T16:12:08Z","file_size":1201840,"file_name":"2018_ProbTheory_Ajanki.pdf","file_id":"5720","date_updated":"2020-07-14T12:46:26Z","creator":"dernst","relation":"main_file","access_level":"open_access","checksum":"f9354fa5c71f9edd17132588f0dc7d01"}],"department":[{"_id":"LaEr"}],"ddc":["510"],"_id":"429","article_processing_charge":"Yes (via OA deal)","oa":1,"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."}],"publist_id":"7394","article_type":"original","publication_identifier":{"eissn":["14322064"],"issn":["01788051"]},"publication":"Probability Theory and Related Fields","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"}],"has_accepted_license":"1","scopus_import":1,"issue":"1-2","volume":173,"ec_funded":1,"date_published":"2019-02-01T00:00:00Z","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).\r\n","status":"public","publication_status":"published","doi":"10.1007/s00440-018-0835-z","page":"293–373","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"language":[{"iso":"eng"}],"date_created":"2018-12-11T11:46:25Z","intvolume":" 173","publisher":"Springer","type":"journal_article","title":"Stability of the matrix Dyson equation and random matrices with correlations","year":"2019","file_date_updated":"2020-07-14T12:46:26Z","date_updated":"2021-01-12T07:55:53Z","quality_controlled":"1","day":"01","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","citation":{"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","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.","short":"O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields 173 (2019) 293–373.","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","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.","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."},"author":[{"id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87","full_name":"Ajanki, Oskari H","first_name":"Oskari H","last_name":"Ajanki"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","first_name":"Torben H","last_name":"Krüger"}]},{"language":[{"iso":"eng"}],"page":"65 - 80","type":"journal_article","intvolume":" 84","publisher":"Bolyai Institute","date_created":"2018-12-11T11:45:36Z","date_updated":"2021-01-12T07:00:08Z","quality_controlled":"1","title":"Maps on probability measures preserving certain distances - a survey and some new results","year":"2018","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1802.03305"}],"author":[{"first_name":"Daniel","full_name":"Virosztek, Daniel","orcid":"0000-0003-1109-5511","last_name":"Virosztek","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"citation":{"short":"D. Virosztek, Acta Scientiarum Mathematicarum (Szeged) 84 (2018) 65–80.","ama":"Virosztek D. Maps on probability measures preserving certain distances - a survey and some new results. *Acta Scientiarum Mathematicarum (Szeged)*. 2018;84(1-2):65-80. doi:10.14232/actasm-018-753-y","mla":"Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances - a Survey and Some New Results.” *Acta Scientiarum Mathematicarum (Szeged)*, vol. 84, no. 1–2, Bolyai Institute, 2018, pp. 65–80, doi: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 (Szeged). 84(1–2), 65–80.","ieee":"D. Virosztek, “Maps on probability measures preserving certain distances - a survey and some new results,” *Acta Scientiarum Mathematicarum (Szeged)*, vol. 84, no. 1–2. Bolyai Institute, pp. 65–80, 2018.","chicago":"Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances - a Survey and Some New Results.” *Acta Scientiarum Mathematicarum (Szeged)*. Bolyai Institute, 2018. https://doi.org/10.14232/actasm-018-753-y.","apa":"Virosztek, D. (2018). Maps on probability measures preserving certain distances - a survey and some new results. *Acta Scientiarum Mathematicarum (Szeged)*. Bolyai Institute. https://doi.org/10.14232/actasm-018-753-y"},"external_id":{"arxiv":["1802.03305"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"04","department":[{"_id":"LaEr"}],"month":"06","oa_version":"Preprint","publication":"Acta Scientiarum Mathematicarum (Szeged)","project":[{"grant_number":"291734","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme"}],"oa":1,"_id":"284","abstract":[{"lang":"eng","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."}],"publist_id":"7615","scopus_import":1,"issue":"1-2","doi":"10.14232/actasm-018-753-y","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).","publication_status":"published","status":"public","ec_funded":1,"date_published":"2018-06-04T00:00:00Z","volume":84},{"language":[{"iso":"eng"}],"page":"3271 - 3290","type":"journal_article","intvolume":" 50","publisher":"Society for Industrial and Applied Mathematics ","date_created":"2018-12-11T11:45:03Z","quality_controlled":"1","date_updated":"2021-01-12T06:53:21Z","main_file_link":[{"url":"https://arxiv.org/abs/1708.01546","open_access":"1"}],"year":"2018","title":"Power law decay for systems of randomly coupled differential equations","external_id":{"arxiv":["1708.01546"]},"author":[{"full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Krüger","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Renfrew","orcid":"0000-0003-3493-121X","full_name":"Renfrew, David T","first_name":"David T","id":"4845BF6A-F248-11E8-B48F-1D18A9856A87"}],"citation":{"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.","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.","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","short":"L. Erdös, T.H. Krüger, D.T. Renfrew, SIAM Journal on Mathematical Analysis 50 (2018) 3271–3290.","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","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.","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."},"day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"LaEr"}],"month":"01","oa_version":"Published Version","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804"},{"grant_number":"M02080","name":"Structured Non-Hermitian Random Matrices","_id":"258F40A4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"publication":"SIAM Journal on Mathematical Analysis","publist_id":"7740","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"}],"_id":"181","oa":1,"issue":"3","scopus_import":1,"doi":"10.1137/17M1143125","publication_status":"published","status":"public","acknowledgement":"The work of the second author was also partially supported by the Hausdorff Center of Mathematics.","date_published":"2018-01-01T00:00:00Z","ec_funded":1,"volume":50},{"publication_status":"published","status":"public","doi":"10.1007/s00023-018-0723-1","volume":19,"date_published":"2018-11-13T00:00:00Z","ec_funded":1,"scopus_import":1,"issue":"12","has_accepted_license":"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","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"}],"publication":"Annales Henri Poincare","publication_identifier":{"issn":["14240637"]},"ddc":["500"],"publist_id":"7258","_id":"556","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."}],"article_processing_charge":"Yes (via OA deal)","oa":1,"department":[{"_id":"LaEr"},{"_id":"JaMa"}],"file":[{"date_created":"2019-01-21T15:18:55Z","content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"0c38abe73569b7166b7487ad5d23cc68","file_size":3084674,"file_name":"2018_Annales_Betea.pdf","file_id":"5866","date_updated":"2020-07-14T12:47:03Z","creator":"dernst"}],"oa_version":"Published Version","month":"11","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","day":"13","citation":{"short":"D. Betea, J. Bouttier, P. Nejjar, M. Vuletic, Annales Henri Poincare 19 (2018) 3663–3742.","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.","mla":"Betea, Dan, et al. “The Free Boundary Schur Process and Applications I.” *Annales Henri Poincare*, vol. 19, no. 12, Fakultät für Mathematik Universität Wien, 2018, pp. 3663–742, doi: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","apa":"Betea, D., Bouttier, J., Nejjar, P., & Vuletic, M. (2018). The free boundary Schur process and applications I. *Annales Henri Poincare*. Fakultät für Mathematik Universität Wien. https://doi.org/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*. Fakultät für Mathematik Universität Wien, 2018. https://doi.org/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. Fakultät für Mathematik Universität Wien, pp. 3663–3742, 2018."},"author":[{"last_name":"Betea","first_name":"Dan","full_name":"Betea, Dan"},{"full_name":"Bouttier, Jeremie","first_name":"Jeremie","last_name":"Bouttier"},{"id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","full_name":"Nejjar, Peter","first_name":"Peter","last_name":"Nejjar"},{"full_name":"Vuletic, Mirjana","first_name":"Mirjana","last_name":"Vuletic"}],"quality_controlled":"1","date_updated":"2021-01-12T08:02:43Z","year":"2018","title":"The free boundary Schur process and applications I","file_date_updated":"2020-07-14T12:47:03Z","type":"journal_article","date_created":"2018-12-11T11:47:09Z","publisher":"Fakultät für Mathematik Universität Wien","intvolume":" 19","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"language":[{"iso":"eng"}],"page":"3663-3742"},{"main_file_link":[{"url":"https://arxiv.org/abs/1612.07776 ","open_access":"1"}],"year":"2018","title":"Local inhomogeneous circular law","quality_controlled":"1","date_updated":"2021-01-12T08:03:07Z","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","day":"03","author":[{"full_name":"Alt, Johannes","first_name":"Johannes","last_name":"Alt","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"last_name":"Krüger","first_name":"Torben H","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87"}],"citation":{"ista":"Alt J, Erdös L, Krüger TH. 2018. Local inhomogeneous circular law. Annals Applied Probability . 28(1), 148–203.","ama":"Alt J, Erdös L, Krüger TH. Local inhomogeneous circular law. *Annals Applied Probability *. 2018;28(1):148-203. doi: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.","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","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.","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."},"external_id":{"arxiv":["1612.07776 "]},"page":"148-203","related_material":{"record":[{"id":"149","relation":"dissertation_contains","status":"public"}]},"language":[{"iso":"eng"}],"date_created":"2018-12-11T11:47:13Z","publisher":"Institute of Mathematical Statistics","intvolume":" 28","type":"journal_article","scopus_import":1,"issue":"1","volume":28,"date_published":"2018-03-03T00:00:00Z","ec_funded":1,"publication_status":"published","status":"public","doi":"10.1214/17-AAP1302","oa_version":"Preprint","month":"03","department":[{"_id":"LaEr"}],"_id":"566","abstract":[{"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","lang":"eng"}],"article_processing_charge":"No","oa":1,"article_type":"original","project":[{"grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems"}],"publication":"Annals Applied Probability "},{"date_updated":"2021-01-12T08:05:25Z","quality_controlled":"1","scopus_import":1,"article_number":"1950009","year":"2018","title":"Bounds on the norm of Wigner-type random matrices","main_file_link":[{"url":"https://arxiv.org/abs/1802.05175","open_access":"1"}],"doi":"10.1142/s2010326319500096","status":"public","publication_status":"published","citation":{"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.","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.","short":"L. Erdös, P. Mühlbacher, Random Matrices: Theory and Applications (2018).","ista":"Erdös L, Mühlbacher P. 2018. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications., 1950009.","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.","ama":"Erdös L, Mühlbacher P. Bounds on the norm of Wigner-type random matrices. *Random matrices: Theory and applications*. 2018. doi:10.1142/s2010326319500096"},"ec_funded":1,"author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","last_name":"Erdös"},{"last_name":"Mühlbacher","first_name":"Peter","full_name":"Mühlbacher, Peter"}],"external_id":{"arxiv":["1802.05175"]},"date_published":"2018-09-26T00:00:00Z","day":"26","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"department":[{"_id":"LaEr"}],"month":"09","oa_version":"Preprint","publication_identifier":{"issn":["2010-3263","2010-3271"]},"publication":"Random matrices: Theory and applications","project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"type":"journal_article","oa":1,"_id":"5971","publisher":"World Scientific Publishing","abstract":[{"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.","lang":"eng"}],"date_created":"2019-02-13T10:40:54Z"},{"author":[{"id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","last_name":"Alt","first_name":"Johannes","full_name":"Alt, Johannes"},{"last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Krüger","full_name":"Krüger, Torben H","first_name":"Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"arxiv":["1804.07752"]},"citation":{"chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” *ArXiv*, n.d.","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy: Spectral bands, edges and cusps,” *arXiv*. .","apa":"Alt, J., Erdös, L., & Krüger, T. H. (n.d.). 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*.","mla":"Alt, Johannes, et al. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” *ArXiv*, 1804.07752.","ista":"Alt J, Erdös L, Krüger TH. 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.)."},"date_published":"2018-04-20T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"20","status":"public","publication_status":"submitted","title":"The Dyson equation with linear self-energy: Spectral bands, edges and cusps","year":"2018","article_number":"1804.07752","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.07752"}],"date_updated":"2021-01-12T08:06:36Z","_id":"6183","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"}],"oa":1,"article_processing_charge":"No","date_created":"2019-03-28T09:20:06Z","publication":"arXiv","type":"preprint","month":"04","oa_version":"Preprint","language":[{"iso":"eng"}],"related_material":{"record":[{"id":"149","relation":"dissertation_contains","status":"public"}]},"department":[{"_id":"LaEr"}]},{"language":[{"iso":"eng"}],"type":"journal_article","intvolume":" 171","publisher":"Springer","date_created":"2018-12-11T11:47:56Z","date_updated":"2021-01-12T08:09:33Z","quality_controlled":"1","year":"2018","title":"Local law and Tracy–Widom limit for sparse random matrices","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1605.08767"}],"external_id":{"arxiv":["1605.08767"]},"author":[{"first_name":"Jii","full_name":"Lee, Jii","last_name":"Lee"},{"first_name":"Kevin","full_name":"Schnelli, Kevin","orcid":"0000-0003-0954-3231","last_name":"Schnelli","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87"}],"citation":{"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.","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.","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.","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.","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","short":"J. Lee, K. Schnelli, Probability Theory and Related Fields 171 (2018)."},"day":"14","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"LaEr"}],"month":"06","oa_version":"Preprint","publication":"Probability Theory and Related Fields","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"_id":"690","abstract":[{"lang":"eng","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."}],"oa":1,"publist_id":"7017","issue":"1-2","scopus_import":1,"article_number":"543-616","doi":"10.1007/s00440-017-0787-8","publication_status":"published","status":"public","ec_funded":1,"date_published":"2018-06-14T00:00:00Z","volume":171},{"issue":"2","scopus_import":1,"has_accepted_license":"1","publication_status":"published","status":"public","doi":"10.30757/ALEA.v15-49","volume":15,"date_published":"2018-10-01T00:00:00Z","ec_funded":1,"department":[{"_id":"LaEr"},{"_id":"JaMa"}],"file":[{"date_created":"2019-02-14T09:44:10Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","checksum":"2ded46aa284a836a8cbb34133a64f1cb","file_size":394851,"creator":"kschuh","date_updated":"2020-07-14T12:47:46Z","file_name":"2018_ALEA_Nejjar.pdf","file_id":"5981"}],"oa_version":"Published Version","month":"10","article_type":"original","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"},{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"}],"publication":"Latin American Journal of Probability and Mathematical Statistics","publication_identifier":{"issn":["1980-0436"]},"ddc":["510"],"_id":"70","oa":1,"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."}],"article_processing_charge":"No","quality_controlled":"1","date_updated":"2021-01-12T08:11:24Z","year":"2018","title":"Transition to shocks in TASEP and decoupling of last passage times","file_date_updated":"2020-07-14T12:47:46Z","day":"01","user_id":"D865714E-FA4E-11E9-B85B-F5C5E5697425","author":[{"full_name":"Nejjar, Peter","first_name":"Peter","last_name":"Nejjar","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87"}],"citation":{"chicago":"Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” *Latin American Journal of Probability and Mathematical Statistics*. ALEA, 2018. https://doi.org/10.30757/ALEA.v15-49.","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. ALEA, 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*. ALEA. https://doi.org/10.30757/ALEA.v15-49","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","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, ALEA, 2018, pp. 1311–34, 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.","short":"P. Nejjar, Latin American Journal of Probability and Mathematical Statistics 15 (2018) 1311–1334."},"external_id":{"arxiv":["1705.08836"]},"language":[{"iso":"eng"}],"page":"1311-1334","type":"journal_article","date_created":"2018-12-11T11:44:28Z","intvolume":" 15","publisher":"ALEA"},{"publist_id":"7772","_id":"149","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."}],"oa":1,"ddc":["515","519"],"project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"month":"07","supervisor":[{"last_name":"Erdös","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"}],"oa_version":"Published Version","department":[{"_id":"LaEr"}],"file":[{"file_name":"2018_thesis_Alt.pdf","file_id":"6241","date_updated":"2020-07-14T12:44:57Z","creator":"dernst","file_size":5801709,"relation":"main_file","checksum":"d4dad55a7513f345706aaaba90cb1bb8","access_level":"open_access","content_type":"application/pdf","date_created":"2019-04-08T13:55:20Z"},{"access_level":"closed","relation":"source_file","checksum":"d73fcf46300dce74c403f2b491148ab4","file_size":3802059,"file_name":"2018_thesis_Alt_source.zip","file_id":"6242","date_updated":"2020-07-14T12:44:57Z","creator":"dernst","date_created":"2019-04-08T13:55:20Z","content_type":"application/zip"}],"date_published":"2018-07-12T00:00:00Z","ec_funded":1,"doi":"10.15479/AT:ISTA:TH_1040","publication_status":"published","status":"public","has_accepted_license":"1","pubrep_id":"1040","publisher":"IST Austria","date_created":"2018-12-11T11:44:53Z","type":"dissertation","page":"456","language":[{"iso":"eng"}],"related_material":{"record":[{"status":"public","id":"1010","relation":"part_of_dissertation"},{"id":"1677","relation":"part_of_dissertation","status":"public"},{"id":"550","relation":"part_of_dissertation","status":"public"},{"status":"public","id":"566","relation":"part_of_dissertation"},{"status":"public","id":"6183","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"6184","status":"public"},{"id":"6240","relation":"part_of_dissertation","status":"public"}]},"alternative_title":["IST Austria Thesis"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"citation":{"apa":"Alt, J. (2018). *Dyson equation and eigenvalue statistics of random matrices*. IST Austria. https://doi.org/10.15479/AT:ISTA:TH_1040","chicago":"Alt, Johannes. “Dyson Equation and Eigenvalue Statistics of Random Matrices.” IST Austria, 2018. https://doi.org/10.15479/AT:ISTA:TH_1040.","ieee":"J. Alt, “Dyson equation and eigenvalue statistics of random matrices,” IST Austria, 2018.","short":"J. Alt, Dyson Equation and Eigenvalue Statistics of Random Matrices, IST Austria, 2018.","ista":"Alt J. 2018. Dyson equation and eigenvalue statistics of random matrices. IST Austria.","ama":"Alt J. Dyson equation and eigenvalue statistics of random matrices. 2018. doi:10.15479/AT:ISTA:TH_1040","mla":"Alt, Johannes. *Dyson Equation and Eigenvalue Statistics of Random Matrices*. IST Austria, 2018, doi:10.15479/AT:ISTA:TH_1040."},"author":[{"first_name":"Johannes","full_name":"Alt, Johannes","last_name":"Alt","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"12","file_date_updated":"2020-07-14T12:44:57Z","title":"Dyson equation and eigenvalue statistics of random matrices","year":"2018","date_updated":"2021-01-12T08:06:48Z"},{"status":"public","publication_status":"published","doi":"10.1093/imrn/rnw330","volume":2018,"ec_funded":1,"date_published":"2018-05-18T00:00:00Z","issue":"10","scopus_import":1,"publication":"International Mathematics Research Notices","publication_identifier":{"issn":["10737928"]},"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804"}],"oa":1,"_id":"1012","abstract":[{"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.","lang":"eng"}],"publist_id":"6383","department":[{"_id":"LaEr"}],"oa_version":"Preprint","month":"05","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"18","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.","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.","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.","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.","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"},"author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös"},{"full_name":"Schröder, Dominik J","first_name":"Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"arxiv":["1608.05163"]},"date_updated":"2021-01-12T08:06:34Z","quality_controlled":"1","title":"Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues","year":"2018","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.05163"}],"type":"journal_article","date_created":"2018-12-11T11:49:41Z","publisher":"Oxford University Press","intvolume":" 2018","language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"dissertation_contains","id":"6179","status":"public"}]},"page":"3255-3298"},{"status":"public","publication_status":"published","doi":"10.1002/cpa.21639","volume":70,"ec_funded":1,"date_published":"2017-09-01T00:00:00Z","issue":"9","scopus_import":1,"publication":"Communications on Pure and Applied Mathematics","publication_identifier":{"issn":["00103640"]},"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":"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."}],"_id":"721","oa":1,"publist_id":"6959","department":[{"_id":"LaEr"}],"oa_version":"Submitted Version","month":"09","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","day":"01","author":[{"last_name":"Ajanki","first_name":"Oskari H","full_name":"Ajanki, Oskari H","id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","first_name":"Torben H","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Erdös","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"}],"citation":{"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.","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.","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.","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.","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"},"date_updated":"2021-01-12T08:12:24Z","quality_controlled":"1","title":"Singularities of solutions to quadratic vector equations on the complex upper half plane","year":"2017","main_file_link":[{"url":"https://arxiv.org/abs/1512.03703","open_access":"1"}],"type":"journal_article","date_created":"2018-12-11T11:48:08Z","publisher":"Wiley-Blackwell","intvolume":" 70","language":[{"iso":"eng"}],"page":"1672 - 1705"},{"publist_id":"6935","_id":"733","oa":1,"abstract":[{"lang":"eng","text":"Let A and B be two N by N deterministic Hermitian matrices and let U be an N by N Haar distributed unitary matrix. It is well known that the spectral distribution of the sum H = A + UBU∗ converges weakly to the free additive convolution of the spectral distributions of A and B, as N tends to infinity. We establish the optimal convergence rate in the bulk of the spectrum."}],"project":[{"grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems"}],"publication":"Advances in Mathematics","oa_version":"Submitted Version","month":"10","department":[{"_id":"LaEr"}],"volume":319,"date_published":"2017-10-15T00:00:00Z","ec_funded":1,"publication_status":"published","status":"public","acknowledgement":"Partially supported by ERC Advanced Grant RANMAT No. 338804, Hong Kong RGC grant ECS 26301517, and the Göran Gustafsson Foundation","doi":"10.1016/j.aim.2017.08.028","scopus_import":1,"date_created":"2018-12-11T11:48:13Z","publisher":"Academic Press","intvolume":" 319","type":"journal_article","page":"251 - 291","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"15","citation":{"short":"Z. Bao, L. Erdös, K. Schnelli, Advances in Mathematics 319 (2017) 251–291.","ista":"Bao Z, Erdös L, Schnelli K. 2017. Convergence rate for spectral distribution of addition of random matrices. Advances in Mathematics. 319, 251–291.","mla":"Bao, Zhigang, et al. “Convergence Rate for Spectral Distribution of Addition of Random Matrices.” *Advances in Mathematics*, vol. 319, Academic Press, 2017, pp. 251–91, doi:10.1016/j.aim.2017.08.028.","ama":"Bao Z, Erdös L, Schnelli K. Convergence rate for spectral distribution of addition of random matrices. *Advances in Mathematics*. 2017;319:251-291. doi:10.1016/j.aim.2017.08.028","apa":"Bao, Z., Erdös, L., & Schnelli, K. (2017). Convergence rate for spectral distribution of addition of random matrices. *Advances in Mathematics*. Academic Press. https://doi.org/10.1016/j.aim.2017.08.028","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Convergence rate for spectral distribution of addition of random matrices,” *Advances in Mathematics*, vol. 319. Academic Press, pp. 251–291, 2017.","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Convergence Rate for Spectral Distribution of Addition of Random Matrices.” *Advances in Mathematics*. Academic Press, 2017. https://doi.org/10.1016/j.aim.2017.08.028."},"author":[{"last_name":"Bao","orcid":"0000-0003-3036-1475","first_name":"Zhigang","full_name":"Bao, Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Schnelli","orcid":"0000-0003-0954-3231","first_name":"Kevin","full_name":"Schnelli, Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87"}],"main_file_link":[{"url":"https://arxiv.org/abs/1606.03076","open_access":"1"}],"title":"Convergence rate for spectral distribution of addition of random matrices","year":"2017","quality_controlled":"1","date_updated":"2021-01-12T08:13:07Z"},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1602.02312"}],"title":"Universality for a class of random band matrices","year":"2017","quality_controlled":"1","date_updated":"2021-01-12T08:00:57Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"25","author":[{"last_name":"Bourgade","first_name":"Paul","full_name":"Bourgade, Paul"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","last_name":"Erdös"},{"last_name":"Yau","full_name":"Yau, Horng","first_name":"Horng"},{"last_name":"Yin","full_name":"Yin, Jun","first_name":"Jun"}],"citation":{"short":"P. Bourgade, L. Erdös, H. Yau, J. Yin, Advances in Theoretical and Mathematical Physics 21 (2017) 739–800.","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.","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.","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","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.","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","language":[{"iso":"eng"}],"date_created":"2018-12-11T11:46:43Z","intvolume":" 21","publisher":"International Press","type":"journal_article","issue":"3","scopus_import":1,"volume":21,"date_published":"2017-08-25T00:00:00Z","ec_funded":1,"publication_status":"published","status":"public","doi":"10.4310/ATMP.2017.v21.n3.a5","oa_version":"Submitted Version","month":"08","department":[{"_id":"LaEr"}],"publist_id":"7337","_id":"483","oa":1,"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"}],"project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"publication":"Advances in Theoretical and Mathematical Physics","publication_identifier":{"issn":["10950761"]}},{"language":[{"iso":"eng"}],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"149"}]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","pubrep_id":"926","publisher":"Institute of Mathematical Statistics","intvolume":" 22","date_created":"2018-12-11T11:47:07Z","quality_controlled":"1","date_updated":"2021-01-12T08:02:34Z","file_date_updated":"2020-07-14T12:47:00Z","title":"Singularities of the density of states of random Gram matrices","year":"2017","citation":{"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","ieee":"J. Alt, “Singularities of the density of states of random Gram matrices,” *Electronic Communications in Probability*, vol. 22. Institute of Mathematical Statistics, 2017.","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.","ista":"Alt J. 2017. Singularities of the density of states of random Gram matrices. Electronic Communications in Probability. 22, 63.","ama":"Alt J. Singularities of the density of states of random Gram matrices. *Electronic Communications in Probability*. 2017;22. doi:10.1214/17-ECP97","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.","short":"J. Alt, Electronic Communications in Probability 22 (2017)."},"author":[{"last_name":"Alt","first_name":"Johannes","full_name":"Alt, Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"21","department":[{"_id":"LaEr"}],"file":[{"checksum":"0ec05303a0de190de145654237984c79","access_level":"open_access","relation":"main_file","file_size":470876,"file_name":"IST-2018-926-v1+1_euclid.ecp.1511233247.pdf","file_id":"4663","creator":"system","date_updated":"2020-07-14T12:47:00Z","date_created":"2018-12-12T10:08:04Z","content_type":"application/pdf"}],"month":"11","oa_version":"Published Version","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"}],"publication":"Electronic Communications in Probability","publication_identifier":{"issn":["1083589X"]},"publist_id":"7265","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."}],"_id":"550","oa":1,"ddc":["539"],"scopus_import":1,"has_accepted_license":"1","article_number":"63","doi":"10.1214/17-ECP97","publication_status":"published","status":"public","date_published":"2017-11-21T00:00:00Z","ec_funded":1,"volume":22},{"day":"01","volume":28,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"citation":{"apa":"Erdös, L., & Yau, H. (2017). *A dynamical approach to random matrix theory* (Vol. 28). American Mathematical Society.","ieee":"L. Erdös and H. Yau, *A dynamical approach to random matrix theory*, vol. 28. 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.","ista":"Erdös L, Yau H. 2017. A dynamical approach to random matrix theory, American Mathematical Society, 226p.","mla":"Erdös, László, and Horng Yau. *A Dynamical Approach to Random Matrix Theory*. Vol. 28, American Mathematical Society, 2017.","ama":"Erdös L, Yau H. *A Dynamical Approach to Random Matrix Theory*. Vol 28. American Mathematical Society; 2017.","short":"L. Erdös, H. Yau, A Dynamical Approach to Random Matrix Theory, American Mathematical Society, 2017."},"author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"last_name":"Yau","full_name":"Yau, Horng","first_name":"Horng"}],"date_published":"2017-01-01T00:00:00Z","status":"public","publication_status":"published","title":"A dynamical approach to random matrix theory","year":"2017","date_updated":"2020-01-16T12:37:45Z","quality_controlled":"1","date_created":"2018-12-11T11:47:13Z","_id":"567","abstract":[{"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","lang":"eng"}],"publisher":"American Mathematical Society","intvolume":" 28","publist_id":"7247","type":"book","publication_identifier":{"eisbn":["978-1-4704-4194-4"],"isbn":["9781470436483"]},"project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"oa_version":"None","series_title":"Courant Lecture Notes","page":"226","month":"01","department":[{"_id":"LaEr"}],"alternative_title":["Courant Lecture Notes"],"language":[{"iso":"eng"}]},{"publisher":"Institute of Mathematical Statistics","intvolume":" 53","date_created":"2018-12-11T11:47:30Z","type":"journal_article","page":"1606 - 1656","language":[{"iso":"eng"}],"citation":{"short":"L. Erdös, K. Schnelli, Annales de l’institut Henri Poincare (B) Probability and Statistics 53 (2017) 1606–1656.","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.","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","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.","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.","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.","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"},"author":[{"full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0003-0954-3231","first_name":"Kevin","full_name":"Schnelli, Kevin","last_name":"Schnelli","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87"}],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","day":"01","main_file_link":[{"url":"https://arxiv.org/abs/1504.00650","open_access":"1"}],"title":"Universality for random matrix flows with time dependent density","year":"2017","quality_controlled":"1","date_updated":"2021-01-12T08:06:22Z","publist_id":"7189","abstract":[{"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.","lang":"eng"}],"_id":"615","oa":1,"project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"publication_identifier":{"issn":["02460203"]},"publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","month":"11","oa_version":"Submitted Version","department":[{"_id":"LaEr"}],"date_published":"2017-11-01T00:00:00Z","ec_funded":1,"volume":53,"doi":"10.1214/16-AIHP765","publication_status":"published","status":"public","issue":"4","scopus_import":1}]