ISSN:
1572-9613
Keywords:
Random matrix
;
integrating density of states
;
statistical mechanics
;
mean field-theory
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract We consider the ensemble of random symmetricn×n matrices specified by an orthogonal invariant probability distribution. We treat this distribution as a Gibbs measure of a mean-field-type model. This allows us to show that the normalized eigenvalue counting function of this ensemble converges in probability to a nonrandom limit asn→∞ and that this limiting distribution is the solution of a certain self-consistent equation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02184872
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