On the statistical mechanics approach in the random matrix theory: Integrated density of states |
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| Authors: | A. Boutet de Monvel L. Pastur M. Shcherbina |
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| Affiliation: | (1) Laboratory of Mathematical Physics and Geometry, Université Paris VII, 75251 Paris Cedex 05, France;(2) Mathematical Division, Institute for Low Temperature Physics, 310164 Kharkov, Ukraine |
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| 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. |
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| Keywords: | Random matrix integrating density of states statistical mechanics mean field-theory |
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