On Spectral Norm of Large Band Random Matrices
Mathematical Physics
2007-05-23 v1 math.MP
Probability
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.
Cite
@article{arxiv.math-ph/0404017,
title = {On Spectral Norm of Large Band Random Matrices},
author = {A. Khorunzhy},
journal= {arXiv preprint arXiv:math-ph/0404017},
year = {2007}
}
Comments
20 pages, 1 figure