[{"_id":"13317","status":"public","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510","530"],"date_updated":"2023-12-13T11:38:44Z","file_date_updated":"2023-07-31T07:49:31Z","department":[{"_id":"LaEr"}],"oa_version":"Published Version","abstract":[{"lang":"eng","text":"We prove the Eigenstate Thermalisation Hypothesis (ETH) for local observables in a typical translation invariant system of quantum spins with L-body interactions, where L is the number of spins. This mathematically verifies the observation first made by Santos and Rigol (Phys Rev E 82(3):031130, 2010, https://doi.org/10.1103/PhysRevE.82.031130) that the ETH may hold for systems with additional translational symmetries for a naturally restricted class of observables. We also present numerical support for the same phenomenon for Hamiltonians with local interaction."}],"month":"07","intvolume":" 190","scopus_import":"1","file":[{"success":1,"file_id":"13325","checksum":"c2ef6b2aecfee1ad6d03fab620507c2c","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"2023_JourStatPhysics_Sugimoto.pdf","date_created":"2023-07-31T07:49:31Z","file_size":612755,"date_updated":"2023-07-31T07:49:31Z","creator":"dernst"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"publication_status":"published","issue":"7","volume":190,"ec_funded":1,"article_number":"128","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Sugimoto, Shoki, et al. “Eigenstate Thermalisation Hypothesis for Translation Invariant Spin Systems.” Journal of Statistical Physics, vol. 190, no. 7, 128, Springer Nature, 2023, doi:10.1007/s10955-023-03132-4.","ama":"Sugimoto S, Henheik SJ, Riabov V, Erdös L. Eigenstate thermalisation hypothesis for translation invariant spin systems. Journal of Statistical Physics. 2023;190(7). doi:10.1007/s10955-023-03132-4","apa":"Sugimoto, S., Henheik, S. J., Riabov, V., & Erdös, L. (2023). Eigenstate thermalisation hypothesis for translation invariant spin systems. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-023-03132-4","short":"S. Sugimoto, S.J. Henheik, V. Riabov, L. Erdös, Journal of Statistical Physics 190 (2023).","ieee":"S. Sugimoto, S. J. Henheik, V. Riabov, and L. Erdös, “Eigenstate thermalisation hypothesis for translation invariant spin systems,” Journal of Statistical Physics, vol. 190, no. 7. Springer Nature, 2023.","chicago":"Sugimoto, Shoki, Sven Joscha Henheik, Volodymyr Riabov, and László Erdös. “Eigenstate Thermalisation Hypothesis for Translation Invariant Spin Systems.” Journal of Statistical Physics. Springer Nature, 2023. https://doi.org/10.1007/s10955-023-03132-4.","ista":"Sugimoto S, Henheik SJ, Riabov V, Erdös L. 2023. Eigenstate thermalisation hypothesis for translation invariant spin systems. Journal of Statistical Physics. 190(7), 128."},"title":"Eigenstate thermalisation hypothesis for translation invariant spin systems","author":[{"last_name":"Sugimoto","full_name":"Sugimoto, Shoki","first_name":"Shoki"},{"last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"},{"first_name":"Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","full_name":"Riabov, Volodymyr","last_name":"Riabov"},{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"}],"external_id":{"isi":["001035677200002"],"arxiv":["2304.04213"]},"article_processing_charge":"Yes (in subscription journal)","acknowledgement":"LE, JH, and VR were supported by ERC Advanced Grant “RMTBeyond” No. 101020331. SS was supported by KAKENHI Grant Number JP22J14935 from the Japan Society for the Promotion of Science (JSPS) and Forefront Physics and Mathematics Program to Drive Transformation (FoPM), a World-leading Innovative Graduate Study (WINGS) Program, the University of Tokyo.\r\nOpen access funding provided by The University of Tokyo.","quality_controlled":"1","publisher":"Springer Nature","oa":1,"day":"21","publication":"Journal of Statistical Physics","has_accepted_license":"1","isi":1,"year":"2023","doi":"10.1007/s10955-023-03132-4","date_published":"2023-07-21T00:00:00Z","date_created":"2023-07-30T22:01:02Z"},{"title":"Spectrum of Lévy–Khintchine random laplacian matrices","author":[{"full_name":"Campbell, Andrew J","last_name":"Campbell","id":"582b06a9-1f1c-11ee-b076-82ffce00dde4","first_name":"Andrew J"},{"full_name":"O’Rourke, Sean","last_name":"O’Rourke","first_name":"Sean"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["001038341000001"],"arxiv":["2210.07927"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Campbell AJ, O’Rourke S. 2023. Spectrum of Lévy–Khintchine random laplacian matrices. Journal of Theoretical Probability.","chicago":"Campbell, Andrew J, and Sean O’Rourke. “Spectrum of Lévy–Khintchine Random Laplacian Matrices.” Journal of Theoretical Probability. Springer Nature, 2023. https://doi.org/10.1007/s10959-023-01275-4.","ieee":"A. J. Campbell and S. O’Rourke, “Spectrum of Lévy–Khintchine random laplacian matrices,” Journal of Theoretical Probability. Springer Nature, 2023.","short":"A.J. Campbell, S. O’Rourke, Journal of Theoretical Probability (2023).","ama":"Campbell AJ, O’Rourke S. Spectrum of Lévy–Khintchine random laplacian matrices. Journal of Theoretical Probability. 2023. doi:10.1007/s10959-023-01275-4","apa":"Campbell, A. J., & O’Rourke, S. (2023). Spectrum of Lévy–Khintchine random laplacian matrices. Journal of Theoretical Probability. Springer Nature. https://doi.org/10.1007/s10959-023-01275-4","mla":"Campbell, Andrew J., and Sean O’Rourke. “Spectrum of Lévy–Khintchine Random Laplacian Matrices.” Journal of Theoretical Probability, Springer Nature, 2023, doi:10.1007/s10959-023-01275-4."},"publisher":"Springer Nature","quality_controlled":"1","oa":1,"acknowledgement":"The first author thanks Yizhe Zhu for pointing out reference [30]. We thank David Renfrew for comments on an earlier draft. We thank the anonymous referee for a careful reading and helpful comments.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","doi":"10.1007/s10959-023-01275-4","date_published":"2023-07-26T00:00:00Z","date_created":"2023-08-06T22:01:13Z","day":"26","publication":"Journal of Theoretical Probability","isi":1,"has_accepted_license":"1","year":"2023","status":"public","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"13975","department":[{"_id":"LaEr"}],"ddc":["510"],"date_updated":"2023-12-13T12:00:50Z","month":"07","scopus_import":"1","main_file_link":[{"url":"https://doi.org/10.1007/s10959-023-01275-4","open_access":"1"}],"oa_version":"Published Version","abstract":[{"lang":"eng","text":"We consider the spectrum of random Laplacian matrices of the form Ln=An−Dn where An\r\n is a real symmetric random matrix and Dn is a diagonal matrix whose entries are equal to the corresponding row sums of An. If An is a Wigner matrix with entries in the domain of attraction of a Gaussian distribution, the empirical spectral measure of Ln is known to converge to the free convolution of a semicircle distribution and a standard real Gaussian distribution. We consider real symmetric random matrices An with independent entries (up to symmetry) whose row sums converge to a purely non-Gaussian infinitely divisible distribution, which fall into the class of Lévy–Khintchine random matrices first introduced by Jung [Trans Am Math Soc, 370, (2018)]. Our main result shows that the empirical spectral measure of Ln converges almost surely to a deterministic limit. A key step in the proof is to use the purely non-Gaussian nature of the row sums to build a random operator to which Ln converges in an appropriate sense. This operator leads to a recursive distributional equation uniquely describing the Stieltjes transform of the limiting empirical spectral measure."}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1572-9230"],"issn":["0894-9840"]},"publication_status":"epub_ahead"},{"article_number":"e74","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ama":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Gaussian fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 2023;11. doi:10.1017/fms.2023.70","apa":"Cipolloni, G., Erdös, L., Henheik, S. J., & Kolupaiev, O. (2023). Gaussian fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2023.70","ieee":"G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Gaussian fluctuations in the equipartition principle for Wigner matrices,” Forum of Mathematics, Sigma, vol. 11. Cambridge University Press, 2023.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Forum of Mathematics, Sigma 11 (2023).","mla":"Cipolloni, Giorgio, et al. “Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” Forum of Mathematics, Sigma, vol. 11, e74, Cambridge University Press, 2023, doi:10.1017/fms.2023.70.","ista":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2023. Gaussian fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 11, e74.","chicago":"Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge University Press, 2023. https://doi.org/10.1017/fms.2023.70."},"title":"Gaussian fluctuations in the equipartition principle for Wigner matrices","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"},{"last_name":"Kolupaiev","full_name":"Kolupaiev, Oleksii","first_name":"Oleksii","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61"}],"external_id":{"arxiv":["2301.05181"],"isi":["001051980200001"]},"article_processing_charge":"Yes","acknowledgement":"G.C. and L.E. gratefully acknowledge many discussions with Dominik Schröder at the preliminary stage of this project, especially his essential contribution to identify the correct generalisation of traceless observables to the deformed Wigner ensembles.\r\nL.E. and J.H. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331.","quality_controlled":"1","publisher":"Cambridge University Press","oa":1,"day":"23","publication":"Forum of Mathematics, Sigma","has_accepted_license":"1","isi":1,"year":"2023","date_published":"2023-08-23T00:00:00Z","doi":"10.1017/fms.2023.70","date_created":"2023-09-17T22:01:09Z","_id":"14343","status":"public","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510"],"date_updated":"2023-12-13T12:24:23Z","file_date_updated":"2023-09-20T11:09:35Z","department":[{"_id":"LaEr"},{"_id":"GradSch"}],"oa_version":"Published Version","abstract":[{"text":"The total energy of an eigenstate in a composite quantum system tends to be distributed equally among its constituents. We identify the quantum fluctuation around this equipartition principle in the simplest disordered quantum system consisting of linear combinations of Wigner matrices. As our main ingredient, we prove the Eigenstate Thermalisation Hypothesis and Gaussian fluctuation for general quadratic forms of the bulk eigenvectors of Wigner matrices with an arbitrary deformation.","lang":"eng"}],"month":"08","intvolume":" 11","scopus_import":"1","file":[{"checksum":"eb747420e6a88a7796fa934151957676","file_id":"14352","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2023-09-20T11:09:35Z","file_name":"2023_ForumMathematics_Cipolloni.pdf","creator":"dernst","date_updated":"2023-09-20T11:09:35Z","file_size":852652}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["2050-5094"]},"publication_status":"published","volume":11,"ec_funded":1},{"doi":"10.1088/1751-8121/acfe62","date_published":"2023-10-11T00:00:00Z","date_created":"2023-10-12T12:42:53Z","day":"11","publication":"Journal of Physics A: Mathematical and Theoretical","has_accepted_license":"1","isi":1,"year":"2023","quality_controlled":"1","publisher":"IOP Publishing","oa":1,"acknowledgement":"J H gratefully acknowledges partial financial support by the ERC Advanced Grant 'RMTBeyond' No. 101020331.","title":"Creation rate of Dirac particles at a point source","author":[{"first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha"},{"first_name":"Roderich","full_name":"Tumulka, Roderich","last_name":"Tumulka"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["001080908000001"],"arxiv":["2211.16606"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Henheik SJ, Tumulka R. 2023. Creation rate of Dirac particles at a point source. Journal of Physics A: Mathematical and Theoretical. 56(44), 445201.","chicago":"Henheik, Sven Joscha, and Roderich Tumulka. “Creation Rate of Dirac Particles at a Point Source.” Journal of Physics A: Mathematical and Theoretical. IOP Publishing, 2023. https://doi.org/10.1088/1751-8121/acfe62.","ama":"Henheik SJ, Tumulka R. Creation rate of Dirac particles at a point source. Journal of Physics A: Mathematical and Theoretical. 2023;56(44). doi:10.1088/1751-8121/acfe62","apa":"Henheik, S. J., & Tumulka, R. (2023). Creation rate of Dirac particles at a point source. Journal of Physics A: Mathematical and Theoretical. IOP Publishing. https://doi.org/10.1088/1751-8121/acfe62","ieee":"S. J. Henheik and R. Tumulka, “Creation rate of Dirac particles at a point source,” Journal of Physics A: Mathematical and Theoretical, vol. 56, no. 44. IOP Publishing, 2023.","short":"S.J. Henheik, R. Tumulka, Journal of Physics A: Mathematical and Theoretical 56 (2023).","mla":"Henheik, Sven Joscha, and Roderich Tumulka. “Creation Rate of Dirac Particles at a Point Source.” Journal of Physics A: Mathematical and Theoretical, vol. 56, no. 44, 445201, IOP Publishing, 2023, doi:10.1088/1751-8121/acfe62."},"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"article_number":"445201","issue":"44","volume":56,"ec_funded":1,"file":[{"file_name":"2023_JourPhysics_Henheik.pdf","date_created":"2023-10-16T07:07:24Z","file_size":721399,"date_updated":"2023-10-16T07:07:24Z","creator":"dernst","success":1,"checksum":"5b68de147dd4c608b71a6e0e844d2ce9","file_id":"14429","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1751-8113"],"eissn":["1751-8121"]},"publication_status":"published","month":"10","intvolume":" 56","scopus_import":"1","oa_version":"Published Version","abstract":[{"text":"Only recently has it been possible to construct a self-adjoint Hamiltonian that involves the creation of Dirac particles at a point source in 3d space. Its definition makes use of an interior-boundary condition. Here, we develop for this Hamiltonian a corresponding theory of the Bohmian configuration. That is, we (non-rigorously) construct a Markov jump process $(Q_t)_{t\\in\\mathbb{R}}$ in the configuration space of a variable number of particles that is $|\\psi_t|^2$-distributed at every time t and follows Bohmian trajectories between the jumps. The jumps correspond to particle creation or annihilation events and occur either to or from a configuration with a particle located at the source. The process is the natural analog of Bell's jump process, and a central piece in its construction is the determination of the rate of particle creation. The construction requires an analysis of the asymptotic behavior of the Bohmian trajectories near the source. We find that the particle reaches the source with radial speed 0, but orbits around the source infinitely many times in finite time before absorption (or after emission).","lang":"eng"}],"file_date_updated":"2023-10-16T07:07:24Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"ddc":["510"],"date_updated":"2023-12-13T13:01:25Z","status":"public","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"14421"},{"department":[{"_id":"LaEr"}],"date_updated":"2024-01-09T08:16:41Z","status":"public","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"type":"journal_article","article_type":"original","_id":"14750","volume":33,"issue":"4","ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1050-5164"]},"publication_status":"published","month":"08","intvolume":" 33","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2010.16083"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"Consider the random matrix model A1/2UBU∗A1/2, where A and B are two N × N deterministic matrices and U is either an N × N Haar unitary or orthogonal random matrix. It is well known that on the macroscopic scale (Invent. Math. 104 (1991) 201–220), the limiting empirical spectral distribution (ESD) of the above model is given by the free multiplicative convolution\r\nof the limiting ESDs of A and B, denoted as μα \u0002 μβ, where μα and μβ are the limiting ESDs of A and B, respectively. In this paper, we study the asymptotic microscopic behavior of the edge eigenvalues and eigenvectors statistics. We prove that both the density of μA \u0002μB, where μA and μB are the ESDs of A and B, respectively and the associated subordination functions\r\nhave a regular behavior near the edges. Moreover, we establish the local laws near the edges on the optimal scale. In particular, we prove that the entries of the resolvent are close to some functionals depending only on the eigenvalues of A, B and the subordination functions with optimal convergence rates. Our proofs and calculations are based on the techniques developed for the additive model A+UBU∗ in (J. Funct. Anal. 271 (2016) 672–719; Comm. Math.\r\nPhys. 349 (2017) 947–990; Adv. Math. 319 (2017) 251–291; J. Funct. Anal. 279 (2020) 108639), and our results can be regarded as the counterparts of (J. Funct. Anal. 279 (2020) 108639) for the multiplicative model. "}],"title":"Local laws for multiplication of random matrices","author":[{"last_name":"Ding","full_name":"Ding, Xiucai","first_name":"Xiucai"},{"id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","first_name":"Hong Chang","last_name":"Ji","full_name":"Ji, Hong Chang"}],"article_processing_charge":"No","external_id":{"arxiv":["2010.16083"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random Matrices.” The Annals of Applied Probability, vol. 33, no. 4, Institute of Mathematical Statistics, 2023, pp. 2981–3009, doi:10.1214/22-aap1882.","ieee":"X. Ding and H. C. Ji, “Local laws for multiplication of random matrices,” The Annals of Applied Probability, vol. 33, no. 4. Institute of Mathematical Statistics, pp. 2981–3009, 2023.","short":"X. Ding, H.C. Ji, The Annals of Applied Probability 33 (2023) 2981–3009.","ama":"Ding X, Ji HC. Local laws for multiplication of random matrices. The Annals of Applied Probability. 2023;33(4):2981-3009. doi:10.1214/22-aap1882","apa":"Ding, X., & Ji, H. C. (2023). Local laws for multiplication of random matrices. The Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/22-aap1882","chicago":"Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random Matrices.” The Annals of Applied Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/22-aap1882.","ista":"Ding X, Ji HC. 2023. Local laws for multiplication of random matrices. The Annals of Applied Probability. 33(4), 2981–3009."},"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"doi":"10.1214/22-aap1882","date_published":"2023-08-01T00:00:00Z","date_created":"2024-01-08T13:03:18Z","page":"2981-3009","day":"01","publication":"The Annals of Applied Probability","year":"2023","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"acknowledgement":"The first author is partially supported by NSF Grant DMS-2113489 and grateful for the AMS-SIMONS travel grant (2020–2023). The second author is supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nThe authors would like to thank the Editor, Associate Editor and an anonymous referee for their many critical suggestions which have significantly improved the paper. We also want to thank Zhigang Bao and Ji Oon Lee for many helpful discussions and comments."},{"isi":1,"year":"2023","day":"01","publication":"The Annals of Applied Probability","page":"677-725","doi":"10.1214/22-aap1826","date_published":"2023-02-01T00:00:00Z","date_created":"2024-01-10T09:23:31Z","acknowledgement":"K. Schnelli was supported by the Swedish Research Council Grants VR-2017-05195, and the Knut and Alice Wallenberg Foundation. Y. Xu was supported by the Swedish Research Council Grant VR-2017-05195 and the ERC Advanced Grant “RMTBeyond” No. 101020331.","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"citation":{"ista":"Schnelli K, Xu Y. 2023. Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. The Annals of Applied Probability. 33(1), 677–725.","chicago":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Sample Covariance Matrices.” The Annals of Applied Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/22-aap1826.","ieee":"K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices,” The Annals of Applied Probability, vol. 33, no. 1. Institute of Mathematical Statistics, pp. 677–725, 2023.","short":"K. Schnelli, Y. Xu, The Annals of Applied Probability 33 (2023) 677–725.","ama":"Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. The Annals of Applied Probability. 2023;33(1):677-725. doi:10.1214/22-aap1826","apa":"Schnelli, K., & Xu, Y. (2023). Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. The Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/22-aap1826","mla":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Sample Covariance Matrices.” The Annals of Applied Probability, vol. 33, no. 1, Institute of Mathematical Statistics, 2023, pp. 677–725, doi:10.1214/22-aap1826."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Schnelli","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin"},{"orcid":"0000-0003-1559-1205","full_name":"Xu, Yuanyuan","last_name":"Xu","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","first_name":"Yuanyuan"}],"article_processing_charge":"No","external_id":{"isi":["000946432400021"],"arxiv":["2108.02728"]},"title":"Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"publication_identifier":{"issn":["1050-5164"]},"publication_status":"published","language":[{"iso":"eng"}],"issue":"1","volume":33,"ec_funded":1,"abstract":[{"text":"We establish a quantitative version of the Tracy–Widom law for the largest eigenvalue of high-dimensional sample covariance matrices. To be precise, we show that the fluctuations of the largest eigenvalue of a sample covariance matrix X∗X converge to its Tracy–Widom limit at a rate nearly N−1/3, where X is an M×N random matrix whose entries are independent real or complex random variables, assuming that both M and N tend to infinity at a constant rate. This result improves the previous estimate N−2/9 obtained by Wang (2019). Our proof relies on a Green function comparison method (Adv. Math. 229 (2012) 1435–1515) using iterative cumulant expansions, the local laws for the Green function and asymptotic properties of the correlation kernel of the white Wishart ensemble.","lang":"eng"}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2108.02728"}],"month":"02","intvolume":" 33","date_updated":"2024-01-10T13:31:46Z","department":[{"_id":"LaEr"}],"_id":"14775","type":"journal_article","article_type":"original","status":"public","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"]},{"publisher":"Elsevier","quality_controlled":"1","oa":1,"acknowledgement":"The authors would like to thank the editor, the associated editor and two anonymous referees for their many critical suggestions which have significantly improved the paper. The authors are also grateful to Zhigang Bao and Ji Oon Lee for many helpful discussions. The first author also wants to thank Hari Bercovici for many useful comments. The first author is partially supported by National Science Foundation DMS-2113489 and the second author is supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","date_published":"2023-09-01T00:00:00Z","doi":"10.1016/j.spa.2023.05.009","date_created":"2024-01-10T09:29:25Z","page":"25-60","day":"01","publication":"Stochastic Processes and their Applications","isi":1,"has_accepted_license":"1","year":"2023","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"title":"Spiked multiplicative random matrices and principal components","author":[{"last_name":"Ding","full_name":"Ding, Xiucai","first_name":"Xiucai"},{"first_name":"Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","full_name":"Ji, Hong Chang","last_name":"Ji"}],"article_processing_charge":"Yes (in subscription journal)","external_id":{"isi":["001113615900001"],"arxiv":["2302.13502"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and Principal Components.” Stochastic Processes and Their Applications, vol. 163, Elsevier, 2023, pp. 25–60, doi:10.1016/j.spa.2023.05.009.","short":"X. Ding, H.C. Ji, Stochastic Processes and Their Applications 163 (2023) 25–60.","ieee":"X. Ding and H. C. Ji, “Spiked multiplicative random matrices and principal components,” Stochastic Processes and their Applications, vol. 163. Elsevier, pp. 25–60, 2023.","ama":"Ding X, Ji HC. Spiked multiplicative random matrices and principal components. Stochastic Processes and their Applications. 2023;163:25-60. doi:10.1016/j.spa.2023.05.009","apa":"Ding, X., & Ji, H. C. (2023). Spiked multiplicative random matrices and principal components. Stochastic Processes and Their Applications. Elsevier. https://doi.org/10.1016/j.spa.2023.05.009","chicago":"Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and Principal Components.” Stochastic Processes and Their Applications. Elsevier, 2023. https://doi.org/10.1016/j.spa.2023.05.009.","ista":"Ding X, Ji HC. 2023. Spiked multiplicative random matrices and principal components. Stochastic Processes and their Applications. 163, 25–60."},"month":"09","intvolume":" 163","oa_version":"Published Version","abstract":[{"text":"In this paper, we study the eigenvalues and eigenvectors of the spiked invariant multiplicative models when the randomness is from Haar matrices. We establish the limits of the outlier eigenvalues λˆi and the generalized components (⟨v,uˆi⟩ for any deterministic vector v) of the outlier eigenvectors uˆi with optimal convergence rates. Moreover, we prove that the non-outlier eigenvalues stick with those of the unspiked matrices and the non-outlier eigenvectors are delocalized. The results also hold near the so-called BBP transition and for degenerate spikes. On one hand, our results can be regarded as a refinement of the counterparts of [12] under additional regularity conditions. On the other hand, they can be viewed as an analog of [34] by replacing the random matrix with i.i.d. entries with Haar random matrix.","lang":"eng"}],"volume":163,"ec_funded":1,"file":[{"creator":"dernst","file_size":1870349,"date_updated":"2024-01-16T08:47:31Z","file_name":"2023_StochasticProcAppl_Ding.pdf","date_created":"2024-01-16T08:47:31Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"14806","checksum":"46a708b0cd5569a73d0f3d6c3e0a44dc"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1879-209X"],"issn":["0304-4149"]},"publication_status":"published","status":"public","keyword":["Applied Mathematics","Modeling and Simulation","Statistics and Probability"],"article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"14780","file_date_updated":"2024-01-16T08:47:31Z","department":[{"_id":"LaEr"}],"ddc":["510"],"date_updated":"2024-01-16T08:49:51Z"},{"abstract":[{"lang":"eng","text":"We establish a precise three-term asymptotic expansion, with an optimal estimate of the error term, for the rightmost eigenvalue of an n×n random matrix with independent identically distributed complex entries as n tends to infinity. All terms in the expansion are universal."}],"oa_version":"Preprint","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2206.04448","open_access":"1"}],"month":"11","intvolume":" 51","publication_identifier":{"issn":["0091-1798"]},"publication_status":"published","language":[{"iso":"eng"}],"issue":"6","volume":51,"ec_funded":1,"_id":"14849","article_type":"original","type":"journal_article","status":"public","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"date_updated":"2024-01-23T10:56:30Z","department":[{"_id":"LaEr"}],"acknowledgement":"The second and the fourth author were supported by the ERC Advanced Grant\r\n“RMTBeyond” No. 101020331. The third author was supported by Dr. Max Rössler, the\r\nWalter Haefner Foundation and the ETH Zürich Foundation.","publisher":"Institute of Mathematical Statistics","quality_controlled":"1","oa":1,"year":"2023","day":"01","publication":"The Annals of Probability","page":"2192-2242","date_published":"2023-11-01T00:00:00Z","doi":"10.1214/23-aop1643","date_created":"2024-01-22T08:08:41Z","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"citation":{"mla":"Cipolloni, Giorgio, et al. “On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” The Annals of Probability, vol. 51, no. 6, Institute of Mathematical Statistics, 2023, pp. 2192–242, doi:10.1214/23-aop1643.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, The Annals of Probability 51 (2023) 2192–2242.","ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “On the rightmost eigenvalue of non-Hermitian random matrices,” The Annals of Probability, vol. 51, no. 6. Institute of Mathematical Statistics, pp. 2192–2242, 2023.","apa":"Cipolloni, G., Erdös, L., Schröder, D. J., & Xu, Y. (2023). On the rightmost eigenvalue of non-Hermitian random matrices. The Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/23-aop1643","ama":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. On the rightmost eigenvalue of non-Hermitian random matrices. The Annals of Probability. 2023;51(6):2192-2242. doi:10.1214/23-aop1643","chicago":"Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” The Annals of Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/23-aop1643.","ista":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2023. On the rightmost eigenvalue of non-Hermitian random matrices. The Annals of Probability. 51(6), 2192–2242."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Yuanyuan","full_name":"Xu, Yuanyuan","last_name":"Xu"}],"external_id":{"arxiv":["2206.04448"]},"article_processing_charge":"No","title":"On the rightmost eigenvalue of non-Hermitian random matrices"},{"date_updated":"2024-03-25T12:48:20Z","citation":{"chicago":"Riabov, Volodymyr. “Mesoscopic Eigenvalue Statistics for Wigner-Type Matrices.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2301.01712.","ista":"Riabov V. Mesoscopic eigenvalue statistics for Wigner-type matrices. arXiv, 2301.01712.","mla":"Riabov, Volodymyr. “Mesoscopic Eigenvalue Statistics for Wigner-Type Matrices.” ArXiv, 2301.01712, doi:10.48550/arXiv.2301.01712.","ama":"Riabov V. Mesoscopic eigenvalue statistics for Wigner-type matrices. arXiv. doi:10.48550/arXiv.2301.01712","apa":"Riabov, V. (n.d.). Mesoscopic eigenvalue statistics for Wigner-type matrices. arXiv. https://doi.org/10.48550/arXiv.2301.01712","short":"V. Riabov, ArXiv (n.d.).","ieee":"V. Riabov, “Mesoscopic eigenvalue statistics for Wigner-type matrices,” arXiv. ."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","last_name":"Riabov","full_name":"Riabov, Volodymyr"}],"external_id":{"arxiv":["2301.01712"]},"article_processing_charge":"No","title":"Mesoscopic eigenvalue statistics for Wigner-type matrices","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"_id":"15128","article_number":"2301.01712","type":"preprint","status":"public","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"publication_status":"submitted","year":"2023","day":"04","language":[{"iso":"eng"}],"publication":"arXiv","date_published":"2023-01-04T00:00:00Z","doi":"10.48550/arXiv.2301.01712","date_created":"2024-03-20T09:41:04Z","ec_funded":1,"abstract":[{"lang":"eng","text":"We prove a universal mesoscopic central limit theorem for linear eigenvalue statistics of a Wigner-type matrix inside the bulk of the spectrum with compactly supported twice continuously differentiable test functions. The main novel ingredient is an optimal local law for the two-point function $T(z,\\zeta)$ and a general class of related quantities involving two resolvents\r\nat nearby spectral parameters. "}],"oa_version":"Preprint","acknowledgement":"Supported by the ERC Advanced Grant ”RMTBeyond” No. 101020331","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2301.01712"}],"oa":1,"month":"01"},{"quality_controlled":"1","publisher":"Society for Industrial and Applied Mathematics","oa":1,"day":"01","publication":"SIAM Journal on Matrix Analysis and Applications","year":"2022","date_published":"2022-07-01T00:00:00Z","doi":"10.1137/21m1424408","date_created":"2023-01-12T12:12:38Z","page":"1469-1487","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Cipolloni, Giorgio, et al. “On the Condition Number of the Shifted Real Ginibre Ensemble.” SIAM Journal on Matrix Analysis and Applications, vol. 43, no. 3, Society for Industrial and Applied Mathematics, 2022, pp. 1469–87, doi:10.1137/21m1424408.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, SIAM Journal on Matrix Analysis and Applications 43 (2022) 1469–1487.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “On the condition number of the shifted real Ginibre ensemble,” SIAM Journal on Matrix Analysis and Applications, vol. 43, no. 3. Society for Industrial and Applied Mathematics, pp. 1469–1487, 2022.","ama":"Cipolloni G, Erdös L, Schröder DJ. On the condition number of the shifted real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. 2022;43(3):1469-1487. doi:10.1137/21m1424408","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). On the condition number of the shifted real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/21m1424408","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Condition Number of the Shifted Real Ginibre Ensemble.” SIAM Journal on Matrix Analysis and Applications. Society for Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/21m1424408.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. On the condition number of the shifted real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. 43(3), 1469–1487."},"title":"On the condition number of the shifted real Ginibre ensemble","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"article_processing_charge":"No","external_id":{"arxiv":["2105.13719"]},"oa_version":"Preprint","abstract":[{"text":"We derive an accurate lower tail estimate on the lowest singular value σ1(X−z) of a real Gaussian (Ginibre) random matrix X shifted by a complex parameter z. Such shift effectively changes the upper tail behavior of the condition number κ(X−z) from the slower (κ(X−z)≥t)≲1/t decay typical for real Ginibre matrices to the faster 1/t2 decay seen for complex Ginibre matrices as long as z is away from the real axis. This sharpens and resolves a recent conjecture in [J. Banks et al., https://arxiv.org/abs/2005.08930, 2020] on the regularizing effect of the real Ginibre ensemble with a genuinely complex shift. As a consequence we obtain an improved upper bound on the eigenvalue condition numbers (known also as the eigenvector overlaps) for real Ginibre matrices. The main technical tool is a rigorous supersymmetric analysis from our earlier work [Probab. Math. Phys., 1 (2020), pp. 101--146].","lang":"eng"}],"month":"07","intvolume":" 43","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2105.13719"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0895-4798"],"eissn":["1095-7162"]},"publication_status":"published","volume":43,"issue":"3","_id":"12179","status":"public","keyword":["Analysis"],"type":"journal_article","article_type":"original","date_updated":"2023-01-27T06:56:06Z","department":[{"_id":"LaEr"}]}]