Spectral measure of heavy tailed band and covariance random matrices

Details Spectral measure of heavy tailed band and covariance random matrices Spectral measure of heavy tailed band and covariance random matrices

2008-11-10

arxiv.org/abs/0811.1587v2

Mathematics

Probability

31 pages, minor modifications, mainly in the regularity argument for Theorem 1.3. To appear in Communications in Mathematical

Scientific paper

We study the asymptotic behavior of the appropriately scaled and possibly perturbed spectral measure $\mu$ of large random real symmetric matrices with heavy tailed entries. Specifically, consider the N by N symmetric matrix $Y_N^\sigma$ whose (i,j) entry is $\sigma(i/N,j/N)X_{ij}$ where $(X_{ij}, 0

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