Open Access
2019 Estimates of norms of log-concave random matrices with dependent entries
Marta Strzelecka
Electron. J. Probab. 24: 1-15 (2019). DOI: 10.1214/19-EJP365


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 and $p'$ denotes the Hölder conjugate of $p$. This generalises a 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 an analogous bound for $m\times n$ random matrices, whose entries form an unconditional vector in $\mathbb{R} ^{mn}$. We also prove bounds for norms of matrices whose entries are certain Gaussian mixtures.


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Marta Strzelecka. "Estimates of norms of log-concave random matrices with dependent entries." Electron. J. Probab. 24 1 - 15, 2019.


Received: 3 April 2019; Accepted: 18 September 2019; Published: 2019
First available in Project Euclid: 2 October 2019

zbMATH: 07142901
MathSciNet: MR4017125
Digital Object Identifier: 10.1214/19-EJP365

Primary: 15B52 , 46B09 , 60B20

Keywords: log-concave vectors , operator norm , random matrices , unconditional vectors

Vol.24 • 2019
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