ON THE STATISTICAL-MECHANICS APPROACH IN THE RANDOM-MATRIX THEORY - INTEGRATED DENSITY-OF-STATES

Authors
DEMONVEL AB PASTUR L SHCHERBINA M
Citation
Ab. Demonvel et al., ON THE STATISTICAL-MECHANICS APPROACH IN THE RANDOM-MATRIX THEORY - INTEGRATED DENSITY-OF-STATES, Journal of statistical physics, 79(3-4), 1995, pp. 585-611
Citations number
18
Categorie Soggetti
Mathematical Method, Physical Science","Physycs, Mathematical
Journal title
Journal of statistical physics → ACNP
ISSN journal
00224715
Volume
79
Issue
3-4
Year of publication
1995
Pages
585 - 611
Database
ISI
SICI code
0022-4715(1995)79:3-4<585:OTSAIT>2.0.ZU;2-6
Abstract
We consider the ensemble of random symmetric n x n matrices specified by an orthogonal invariant probability distribution. We treat this dis tribution as a Gibbs measure of a mean-field-type model. This allows u s to show that the normalized eigenvalue counting function of this ens emble converges in probability to a nonrandom limit as n --> infinity and that this limiting distribution is the solution of a certain self- consistent equation.