Chevet-type inequalities for subexponential Weibull variables and estimates for norms of random matrices
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| Format: | Preprint |
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2023
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| _version_ | 1866912217980469248 |
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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 |
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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 |