Estimates of norms of log-concave random matrices with dependent entries
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866910812334981120 |
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| author | Strzelecka, Marta |
| author_facet | Strzelecka, Marta |
| contents | We prove estimates for $\mathbb{E} \| X: \ell_{p'}^n \to \ell_q^m\|$ for $p,q\ge 2$ and any random matrix $X$ having the entries of the form $a_{ij}Y_{ij}$, where $Y=(Y_{ij})_{1\le i\le m, 1\le j\le n}$ has i.i.d. isotropic log-concave rows. This generalises the result of Guédon, Hinrichs, Litvak, and Prochno for Gaussian matrices with independent entries. Our estimate is optimal up to logarithmic factors. As a byproduct we provide the analogue bound for $m\times n$ random matrices, which entries form an unconditional vector in $\mathbb{R}^{mn}$. We also prove bounds for norms of matrices which entries are certain Gaussian mixtures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1902_01150 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Estimates of norms of log-concave random matrices with dependent entries Strzelecka, Marta Probability Functional Analysis 60B20, 46B09, 15B52 We prove estimates for $\mathbb{E} \| X: \ell_{p'}^n \to \ell_q^m\|$ for $p,q\ge 2$ and any random matrix $X$ having the entries of the form $a_{ij}Y_{ij}$, where $Y=(Y_{ij})_{1\le i\le m, 1\le j\le n}$ has i.i.d. isotropic log-concave rows. This generalises the result of Guédon, Hinrichs, Litvak, and Prochno for Gaussian matrices with independent entries. Our estimate is optimal up to logarithmic factors. As a byproduct we provide the analogue bound for $m\times n$ random matrices, which entries form an unconditional vector in $\mathbb{R}^{mn}$. We also prove bounds for norms of matrices which entries are certain Gaussian mixtures. |
| title | Estimates of norms of log-concave random matrices with dependent entries |
| topic | Probability Functional Analysis 60B20, 46B09, 15B52 |
| url | https://arxiv.org/abs/1902.01150 |