Chevet-type inequalities for subexponential Weibull variables and estimates for norms of random matrices

Fuente: arXiv
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Main Authors: Latała, Rafał, Strzelecka, Marta
Format: Preprint
Published: 2023
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author Latała, Rafał
Strzelecka, Marta
author_facet Latała, Rafał
Strzelecka, Marta
contents We prove two-sided Chevet-type inequalities for independent symmetric Weibull random variables with shape parameter $r\in[1,2]$. We apply them to provide two-sided estimates for operator norms from $\ell_p^n$ to $\ell_q^m$ of random matrices $(a_ib_jX_{i,j})_{i\le m, j\le n}$, in the case when $X_{i,j}$'s are iid symmetric Weibull variables with shape parameter $r\in[1,2]$ or when $X$ is an isotropic log-concave unconditional random matrix. We also show how these Chevet-type inequalities imply two-sided bounds for maximal norms from $\ell_p^n$ to $\ell_q^m$ of submatrices of $X$ in both Weibull and log-concave settings.
format Preprint
id arxiv_https___arxiv_org_abs_2309_04214
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Chevet-type inequalities for subexponential Weibull variables and estimates for norms of random matrices
Latała, Rafał
Strzelecka, Marta
Probability
Functional Analysis
We prove two-sided Chevet-type inequalities for independent symmetric Weibull random variables with shape parameter $r\in[1,2]$. We apply them to provide two-sided estimates for operator norms from $\ell_p^n$ to $\ell_q^m$ of random matrices $(a_ib_jX_{i,j})_{i\le m, j\le n}$, in the case when $X_{i,j}$'s are iid symmetric Weibull variables with shape parameter $r\in[1,2]$ or when $X$ is an isotropic log-concave unconditional random matrix. We also show how these Chevet-type inequalities imply two-sided bounds for maximal norms from $\ell_p^n$ to $\ell_q^m$ of submatrices of $X$ in both Weibull and log-concave settings.
title Chevet-type inequalities for subexponential Weibull variables and estimates for norms of random matrices
topic Probability
Functional Analysis
url https://arxiv.org/abs/2309.04214