DMCA
A generalization of Wigner’s law
| Venue: | Comm. Math. Phys |
| Citations: | 14 - 0 self |
BibTeX
@ARTICLE{Zakharevich_ageneralization,
author = {Inna Zakharevich},
title = {A generalization of Wigner’s law},
journal = {Comm. Math. Phys},
year = {},
pages = {403--414}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
We present a generalization of Wigner's semicircle law: we con-sider a sequence of probability distributions (p1; p2; : : :), with mean value zero and take an N N real symmetric matrix with entries independently chosen from pN and consider analyze the distribution of eigenvalues. If we normalize this distribution by its dispersion we show that as N!1 for certain pN the distribution weakly converges to a universal distribution. The result is a formula for the moments of the universal distribution in terms of the rate of growth of the k-th moment of pN (as a function of N), and describe what this means in terms of the support of the distribution. As a corollary, when pN does not depend on N we obtain Wigner's law: if all moments of a distribution are nite, the distribution of eigenvalues is a semicircle. 1
