[{"arxiv":1,"author":[{"full_name":"Cipolloni, Giorgio","first_name":"Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992"},{"first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","first_name":"Dominik J","full_name":"Schröder, Dominik J"}],"month":"05","publication_identifier":{"eissn":["1097-0312"],"issn":["0010-3640"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"file_size":803440,"relation":"main_file","access_level":"open_access","content_type":"application/pdf","creator":"dernst","date_created":"2023-10-04T09:21:48Z","date_updated":"2023-10-04T09:21:48Z","success":1,"checksum":"8346bc2642afb4ccb7f38979f41df5d9","file_id":"14388","file_name":"2023_CommPureMathematics_Cipolloni.pdf"}],"day":"01","oa_version":"Published Version","status":"public","type":"journal_article","issue":"5","article_processing_charge":"Yes (via OA deal)","date_updated":"2023-10-04T09:22:55Z","oa":1,"title":"Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices","isi":1,"intvolume":"        76","scopus_import":"1","has_accepted_license":"1","language":[{"iso":"eng"}],"publication":"Communications on Pure and Applied Mathematics","publication_status":"published","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)"},"ddc":["510"],"abstract":[{"lang":"eng","text":"We consider large non-Hermitian random matrices X with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are asymptotically Gaussian for test functions having 2+ϵ derivatives. Previously this result was known only for a few special cases; either the test functions were required to be analytic [72], or the distribution of the matrix elements needed to be Gaussian [73], or at least match the Gaussian up to the first four moments [82, 56]. We find the exact dependence of the limiting variance on the fourth cumulant that was not known before. The proof relies on two novel ingredients: (i) a local law for a product of two resolvents of the Hermitisation of X with different spectral parameters and (ii) a coupling of several weakly dependent Dyson Brownian motions. These methods are also the key inputs for our analogous results on the linear eigenvalue statistics of real matrices X that are presented in the companion paper [32]. "}],"external_id":{"isi":["000724652500001"],"arxiv":["1912.04100"]},"project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program","call_identifier":"H2020"}],"date_published":"2023-05-01T00:00:00Z","publisher":"Wiley","volume":76,"quality_controlled":"1","department":[{"_id":"LaEr"}],"page":"946-1034","year":"2023","acknowledgement":"L.E. would like to thank Nathanaël Berestycki and D.S.would like to thank Nina Holden for valuable discussions on the Gaussian freefield.G.C. and L.E. are partially supported by ERC Advanced Grant No. 338804.G.C. received funding from the European Union’s Horizon 2020 research and in-novation programme under the Marie Skłodowska-Curie Grant Agreement No.665385. D.S. is supported by Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation.","date_created":"2021-12-05T23:01:41Z","citation":{"ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices,” <i>Communications on Pure and Applied Mathematics</i>, vol. 76, no. 5. Wiley, pp. 946–1034, 2023.","ama":"Cipolloni G, Erdös L, Schröder DJ. Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. 2023;76(5):946-1034. doi:<a href=\"https://doi.org/10.1002/cpa.22028\">10.1002/cpa.22028</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications on Pure and Applied Mathematics 76 (2023) 946–1034.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Central Limit Theorem for Linear Eigenvalue Statistics of Non-Hermitian Random Matrices.” <i>Communications on Pure and Applied Mathematics</i>. Wiley, 2023. <a href=\"https://doi.org/10.1002/cpa.22028\">https://doi.org/10.1002/cpa.22028</a>.","mla":"Cipolloni, Giorgio, et al. “Central Limit Theorem for Linear Eigenvalue Statistics of Non-Hermitian Random Matrices.” <i>Communications on Pure and Applied Mathematics</i>, vol. 76, no. 5, Wiley, 2023, pp. 946–1034, doi:<a href=\"https://doi.org/10.1002/cpa.22028\">10.1002/cpa.22028</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. 76(5), 946–1034.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. Wiley. <a href=\"https://doi.org/10.1002/cpa.22028\">https://doi.org/10.1002/cpa.22028</a>"},"ec_funded":1,"article_type":"original","_id":"10405","file_date_updated":"2023-10-04T09:21:48Z","doi":"10.1002/cpa.22028"},{"article_type":"original","_id":"8500","language":[{"iso":"eng"}],"publication":"Communications on Pure and Applied Mathematics","doi":"10.1002/cpa.21509","article_processing_charge":"No","year":"2014","issue":"5","date_updated":"2022-08-25T13:58:13Z","keyword":["Applied Mathematics","General Mathematics"],"date_created":"2020-09-18T10:47:01Z","title":"Arnol′d diffusion in a pendulum lattice","citation":{"ista":"Kaloshin V, Levi M, Saprykina M. 2014. Arnol′d diffusion in a pendulum lattice. Communications on Pure and Applied Mathematics. 67(5), 748–775.","mla":"Kaloshin, Vadim, et al. “Arnol′d Diffusion in a Pendulum Lattice.” <i>Communications on Pure and Applied Mathematics</i>, vol. 67, no. 5, Wiley, 2014, pp. 748–75, doi:<a href=\"https://doi.org/10.1002/cpa.21509\">10.1002/cpa.21509</a>.","chicago":"Kaloshin, Vadim, Mark Levi, and Maria Saprykina. “Arnol′d Diffusion in a Pendulum Lattice.” <i>Communications on Pure and Applied Mathematics</i>. Wiley, 2014. <a href=\"https://doi.org/10.1002/cpa.21509\">https://doi.org/10.1002/cpa.21509</a>.","ieee":"V. Kaloshin, M. Levi, and M. Saprykina, “Arnol′d diffusion in a pendulum lattice,” <i>Communications on Pure and Applied Mathematics</i>, vol. 67, no. 5. Wiley, pp. 748–775, 2014.","ama":"Kaloshin V, Levi M, Saprykina M. Arnol′d diffusion in a pendulum lattice. <i>Communications on Pure and Applied Mathematics</i>. 2014;67(5):748-775. doi:<a href=\"https://doi.org/10.1002/cpa.21509\">10.1002/cpa.21509</a>","short":"V. Kaloshin, M. Levi, M. Saprykina, Communications on Pure and Applied Mathematics 67 (2014) 748–775.","apa":"Kaloshin, V., Levi, M., &#38; Saprykina, M. (2014). Arnol′d diffusion in a pendulum lattice. <i>Communications on Pure and Applied Mathematics</i>. Wiley. <a href=\"https://doi.org/10.1002/cpa.21509\">https://doi.org/10.1002/cpa.21509</a>"},"intvolume":"        67","status":"public","type":"journal_article","date_published":"2014-05-01T00:00:00Z","publisher":"Wiley","quality_controlled":"1","volume":67,"page":"748-775","extern":"1","publication_status":"published","author":[{"id":"FE553552-CDE8-11E9-B324-C0EBE5697425","last_name":"Kaloshin","orcid":"0000-0002-6051-2628","first_name":"Vadim","full_name":"Kaloshin, Vadim"},{"last_name":"Levi","full_name":"Levi, Mark","first_name":"Mark"},{"first_name":"Maria","full_name":"Saprykina, Maria","last_name":"Saprykina"}],"month":"05","publication_identifier":{"issn":["0010-3640"]},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","text":"The main model studied in this paper is a lattice of pendula with a nearest‐neighbor coupling. If the coupling is weak, then the system is near‐integrable and KAM tori fill most of the phase space. For all KAM trajectories the energy of each pendulum stays within a narrow band for all time. Still, we show that for an arbitrarily weak coupling of a certain localized type, the neighboring pendula can exchange energy. In fact, the energy can be transferred between the pendula in any prescribed way."}],"oa_version":"None","day":"01"},{"intvolume":"        57","year":"2004","article_processing_charge":"No","issue":"9","date_updated":"2021-01-12T08:19:50Z","keyword":["Applied Mathematics","General Mathematics"],"title":"A limit shape theorem for periodic stochastic dispersion","citation":{"short":"D. Dolgopyat, V. Kaloshin, L. Koralov, Communications on Pure and Applied Mathematics 57 (2004) 1127–1158.","ieee":"D. Dolgopyat, V. Kaloshin, and L. Koralov, “A limit shape theorem for periodic stochastic dispersion,” <i>Communications on Pure and Applied Mathematics</i>, vol. 57, no. 9. Wiley, pp. 1127–1158, 2004.","ama":"Dolgopyat D, Kaloshin V, Koralov L. A limit shape theorem for periodic stochastic dispersion. <i>Communications on Pure and Applied Mathematics</i>. 2004;57(9):1127-1158. doi:<a href=\"https://doi.org/10.1002/cpa.20032\">10.1002/cpa.20032</a>","ista":"Dolgopyat D, Kaloshin V, Koralov L. 2004. A limit shape theorem for periodic stochastic dispersion. Communications on Pure and Applied Mathematics. 57(9), 1127–1158.","mla":"Dolgopyat, Dmitry, et al. “A Limit Shape Theorem for Periodic Stochastic Dispersion.” <i>Communications on Pure and Applied Mathematics</i>, vol. 57, no. 9, Wiley, 2004, pp. 1127–58, doi:<a href=\"https://doi.org/10.1002/cpa.20032\">10.1002/cpa.20032</a>.","chicago":"Dolgopyat, Dmitry, Vadim Kaloshin, and Leonid Koralov. “A Limit Shape Theorem for Periodic Stochastic Dispersion.” <i>Communications on Pure and Applied Mathematics</i>. Wiley, 2004. <a href=\"https://doi.org/10.1002/cpa.20032\">https://doi.org/10.1002/cpa.20032</a>.","apa":"Dolgopyat, D., Kaloshin, V., &#38; Koralov, L. (2004). A limit shape theorem for periodic stochastic dispersion. <i>Communications on Pure and Applied Mathematics</i>. Wiley. <a href=\"https://doi.org/10.1002/cpa.20032\">https://doi.org/10.1002/cpa.20032</a>"},"date_created":"2020-09-18T10:49:12Z","publication":"Communications on Pure and Applied Mathematics","doi":"10.1002/cpa.20032","_id":"8517","article_type":"original","language":[{"iso":"eng"}],"month":"09","publication_identifier":{"issn":["0010-3640","1097-0312"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"text":"We consider the evolution of a connected set on the plane carried by a space periodic incompressible stochastic flow. While for almost every realization of the stochastic flow at time t most of the particles are at a distance of order equation image away from the origin, there is a measure zero set of points that escape to infinity at the linear rate. We study the set of points visited by the original set by time t and show that such a set, when scaled down by the factor of t, has a limiting nonrandom shape.","lang":"eng"}],"oa_version":"None","day":"01","author":[{"first_name":"Dmitry","full_name":"Dolgopyat, Dmitry","last_name":"Dolgopyat"},{"full_name":"Kaloshin, Vadim","first_name":"Vadim","last_name":"Kaloshin","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628"},{"first_name":"Leonid","full_name":"Koralov, Leonid","last_name":"Koralov"}],"publication_status":"published","date_published":"2004-09-01T00:00:00Z","type":"journal_article","status":"public","publisher":"Wiley","quality_controlled":"1","volume":57,"extern":"1","page":"1127-1158"},{"_id":"2731","article_type":"original","doi":"10.1002/(SICI)1097-0312(200006)53:6&lt;667::AID-CPA1&gt;3.0.CO;2-5","citation":{"short":"L. Erdös, H. Yau, Communications on Pure and Applied Mathematics 53 (2000) 667–735.","ama":"Erdös L, Yau H. Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation. <i>Communications on Pure and Applied Mathematics</i>. 2000;53(6):667-735. doi:<a href=\"https://doi.org/10.1002/(SICI)1097-0312(200006)53:6&#38;lt;667::AID-CPA1&#38;gt;3.0.CO;2-5\">10.1002/(SICI)1097-0312(200006)53:6&#38;lt;667::AID-CPA1&#38;gt;3.0.CO;2-5</a>","ieee":"L. Erdös and H. Yau, “Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation,” <i>Communications on Pure and Applied Mathematics</i>, vol. 53, no. 6. Wiley-Blackwell, pp. 667–735, 2000.","mla":"Erdös, László, and Horng Yau. “Linear Boltzmann Equation as the Weak Coupling Limit of a Random Schrödinger Equation.” <i>Communications on Pure and Applied Mathematics</i>, vol. 53, no. 6, Wiley-Blackwell, 2000, pp. 667–735, doi:<a href=\"https://doi.org/10.1002/(SICI)1097-0312(200006)53:6&#38;lt;667::AID-CPA1&#38;gt;3.0.CO;2-5\">10.1002/(SICI)1097-0312(200006)53:6&#38;lt;667::AID-CPA1&#38;gt;3.0.CO;2-5</a>.","ista":"Erdös L, Yau H. 2000. Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation. Communications on Pure and Applied Mathematics. 53(6), 667–735.","chicago":"Erdös, László, and Horng Yau. “Linear Boltzmann Equation as the Weak Coupling Limit of a Random Schrödinger Equation.” <i>Communications on Pure and Applied Mathematics</i>. Wiley-Blackwell, 2000. <a href=\"https://doi.org/10.1002/(SICI)1097-0312(200006)53:6&#38;lt;667::AID-CPA1&#38;gt;3.0.CO;2-5\">https://doi.org/10.1002/(SICI)1097-0312(200006)53:6&#38;lt;667::AID-CPA1&#38;gt;3.0.CO;2-5</a>.","apa":"Erdös, L., &#38; Yau, H. (2000). Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation. <i>Communications on Pure and Applied Mathematics</i>. Wiley-Blackwell. <a href=\"https://doi.org/10.1002/(SICI)1097-0312(200006)53:6&#38;lt;667::AID-CPA1&#38;gt;3.0.CO;2-5\">https://doi.org/10.1002/(SICI)1097-0312(200006)53:6&#38;lt;667::AID-CPA1&#38;gt;3.0.CO;2-5</a>"},"publist_id":"4161","date_created":"2018-12-11T11:59:18Z","acknowledgement":"Partially supported by U.S. National Science Foundation grants DMS-9403462, 9703752. We would like to thank H. Spohn for his several comments and discussions on this project. Part of this work was done during the time when L. E. visited the Erwin Schrödinger Institute in Vienna and when both authors visited the Center of Theoretical Sciences in Taiwan. We thank them for the hospitality and the support of this work.","year":"2000","page":"667 - 735","extern":"1","quality_controlled":"1","volume":53,"publisher":"Wiley-Blackwell","date_published":"2000-06-01T00:00:00Z","publication_status":"published","external_id":{"arxiv":["math-ph/9901020"]},"abstract":[{"text":"We study the time evolution of a quantum particle in a Gaussian random environment. We show that in the weak coupling limit the Wigner distribution of the wave function converges to a solution of a linear Boltzmann equation globally in time. The Boltzmann collision kernel is given by the Born approximation of the quantum differential scattering cross section.","lang":"eng"}],"language":[{"iso":"eng"}],"publication":"Communications on Pure and Applied Mathematics","title":"Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation","date_updated":"2023-05-03T09:09:04Z","article_processing_charge":"No","issue":"6","intvolume":"        53","scopus_import":"1","status":"public","type":"journal_article","author":[{"full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"last_name":"Yau","full_name":"Yau, Horng","first_name":"Horng"}],"arxiv":1,"day":"01","oa_version":"Preprint","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","publication_identifier":{"issn":["0010-3640"]},"month":"06"}]