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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.

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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