On Spectral Norm of Large Band Random Matrices
Abstract
We study the spectral norm of Ndimensional 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.
 Publication:

arXiv eprints
 Pub Date:
 April 2004
 arXiv:
 arXiv:mathph/0404017
 Bibcode:
 2004math.ph...4017K
 Keywords:

 Mathematical Physics;
 Probability;
 15A52
 EPrint:
 20 pages, 1 figure