Some estimates of norms of random matrices

Latała, Rafał

doi:10.1090/S0002-9939-04-07800-1

Some estimates of norms of random matrices
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by Rafał Latała

Proc. Amer. Math. Soc. 133 (2005), 1273-1282

DOI: https://doi.org/10.1090/S0002-9939-04-07800-1

Published electronically: December 15, 2004

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Abstract:

We show that for any random matrix $(X_{ij})$ with independent mean zero entries \[ \mathbf {E}\|(X_{ij})\|\leq C \Big (\max _{i}\sqrt {\sum _{j}\mathbf {E} X_{ij}^{2}}+ \max _{j}\sqrt {\sum _{i}\mathbf {E} X_{ij}^{2}}+ \sqrt [4]{\sum _{ij} \mathbf {E} X_{ij}^{4}} \Big ),\] where $C$ is some universal constant.

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