On Spectral Norm of Large Band Random Matrices

Details On Spectral Norm of Large Band Random Matrices On Spectral Norm of Large Band Random Matrices

2004-04-06

arxiv.org/abs/math-ph/0404017v1

Physics

Mathematical Physics

20 pages, 1 figure

Scientific paper

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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