On the norm and eigenvalue distribution of large random matrices
成果类型：
Article
署名作者：
De Monvel, AB; Khorunzhy, A
署名单位：
Sorbonne Universite; Universite Paris Cite; National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine; National Academy of Sciences Ukraine; B. Verkin Institute for Low Temperature Physics & Engineering of the National Academy of Sciences of Ukraine
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
1999
页码：
913-944
关键词：
摘要：
We study the eigenvalue distribution of NxN symmetric random matrices H-N(x, y) = N(-1/2)h(x, y), x, y = 1,..., N, where h(x, y), x less than or equal to y are Gaussian weakly dependent random variables. We prove that the normalized eigenvalue counting function of H-N converges with probability 1 to a nonrandom function mu(lambda) as N --> infinity. We derive an equation for the Stieltjes transform of the measure d mu(lambda) and show that the latter has a compact support Lambda(mu). We find the upper bound for lim sup(N-->infinity)parallel to H(N)parallel to and study asymptotically the case when there are no eigenvalues of H-N outside of Lambda(mu) when N --> infinity.