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Norms of structured random matrices

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dc.abstract.enFor m,n∈N, let X=(Xij)i≤m,j≤n be a random matrix, A=(aij)i≤m,j≤n a real deterministic matrix, and XA=(aijXij)i≤m,j≤n the corresponding structured random matrix. We study the expected operator norm of XA considered as a random operator between ℓnp and ℓmq for 1≤p,q≤∞. We prove optimal bounds up to logarithmic terms when the underlying random matrix X has i.i.d. Gaussian entries, independent mean-zero bounded entries, or independent mean-zero ψr (r∈(0,2]) entries. In certain cases, we determine the precise order of the expected norm up to constants. Our results are expressed through a sum of operator norms of Hadamard products A∘A and (A∘A)T.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorStrzelecki, Michał
dc.contributor.authorStrzelecka, Marta
dc.contributor.authorProchno, Joscha
dc.contributor.authorAdamczak, Radosław
dc.date.accessioned2024-01-25T13:51:42Z
dc.date.available2024-01-25T13:51:42Z
dc.date.copyright2023-04-09
dc.date.issued2023
dc.description.accesstimeAT_PUBLICATION
dc.description.financeNie dotyczy
dc.description.versionFINAL_PUBLISHED
dc.identifier.doi10.1007/S00208-023-02599-6
dc.identifier.issn0025-5831
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/113910
dc.identifier.weblinkhttps://link.springer.com/content/pdf/10.1007/s00208-023-02599-6.pdf
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofMathematische Annalen
dc.relation.pages1-65
dc.rightsCC-BY
dc.sciencecloudnosend
dc.subject.enGaussian random matrix
dc.subject.enOperator norm
dc.subject.enStructured random matrix
dc.subject.enψr random variable
dc.titleNorms of structured random matrices
dc.typeJournalArticle
dspace.entity.typePublication