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The dimension-free structure of nonhomogeneous random matrices

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dc.abstract.enLet X be a symmetric random matrix with independent but non-identically distributed centered Gaussian entries. We derive two-sided bounds for the expected value of the p-Schatten norm of X for 2≤p≤∞, with constants not depending on p. This settles, in the case p=∞, a conjecture of the first author, and provides a complete characterization of the class of infinite matrices with independent Gaussian entries that define bounded operators on l_2. Along the way, we obtain optimal dimension-free bounds on the L_p norm of the p-Schatten norm of X that are of independent interest. We develop further extensions to non-symmetric matrices and to nonasymptotic moment and norm estimates for matrices with non-Gaussian entries that arise, for example, in the study of random graphs and in applied mathematics.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorLatała, Rafał
dc.contributor.authorHandel, Ramon van
dc.contributor.authorYoussef, Pierre
dc.date.accessioned2024-01-26T10:10:34Z
dc.date.available2024-01-26T10:10:34Z
dc.date.issued2018
dc.description.financeNie dotyczy
dc.description.number3
dc.description.volume214
dc.identifier.doi10.1007/S00222-018-0817-X
dc.identifier.issn0020-9910
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/122116
dc.identifier.weblinkhttps://link.springer.com/article/10.1007/s00222-018-0817-x
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofInventiones Mathematicae
dc.relation.pages1031–1080
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.subject.enrandom matrix operator norm Schatten norm
dc.titleThe dimension-free structure of nonhomogeneous random matrices
dc.typeJournalArticle
dspace.entity.typePublication