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On Spectral Norm of Large Band Random Matrices

A. Khorunzhy
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Abstract

We study the spectral norm of N-dimensional hermitian random matrices whose entries are zero outside of the band of the width b along the principal diagonal. Inside this band the elements are given by gaussian centered jointly independent random variables with the variance of the order 1/b. We show that if b tends to infinity faster than the third power of log N, then the spectral norm is bounded with probability 1.

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A. Khorunzhy. 2004-04-06. On Spectral Norm of Large Band Random Matrices. https://arxiv.org/abs/math-ph/0404017

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