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On the spectral norm of Gaussian random matrices · Around

2015

On the spectral norm of Gaussian random matrices

van Handel, Ramon

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Let $X$ be a $d\times d$ symmetric random matrix with independent but non-identically distributed Gaussian entries.

It has been conjectured by Lata\l{a} that the spectral norm of $X$ is always of the same order as the largest Euclidean norm of its rows.
A positive resolution of this conjecture would provide a sharp understanding of the probabilistic mechanisms that control the spectral norm of inhomogeneous Gaussian random matrices.
This paper establishes the conjecture up to a dimensional factor of order $\sqrt{\log\log d}$.

Built on

The expected norm of random matrices
Y. Seginer · 2000
Earlier work this paper cites.
Some estimates of norms of random matrices
R. Latała · 2005
Earlier work this paper cites.
An introduction to random matrices
G. W. Anderson, A. Guionnet, and O. Zeitouni · 2010
Earlier work this paper cites.

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Then

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