Theory of random matrices with strong level confinement

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dc.creatorFreilikher, V.
dc.creatorKanzieper, E.
dc.creatorYurkevich, I.
dc.date1995-10-02
dc.date1996-04-29
dc.date.accessioned2026-07-07T08:58:58Z
dc.date.available2026-07-07T08:58:58Z
dc.descriptionUnitary ensembles of large N x N random matrices with a non-Gaussian probability distribution P[H] ~ exp{-TrV[H]} are studied using a theory of polynomials orthogonal with respect to exponential weights. Asymptotically exact expressions for density of levels, one- and two-point Green's functions are calculated. We show that in the large-N limit the properly rescaled local eigenvalue correlations are independent of P[H] while global smoothed connected correlations depend on P[H] only through the endpoints of spectrum. We also establish previously unknown intimate connection between structure of Szegö function entering strong polynomial asymptotics and mean-field equation by Dyson.
dc.description4 pages (latex), Several misprints corrected. Extended version available at cond-mat/9604078
dc.identifierhttps://arxiv.org/abs/cond-mat/9510002
dc.identifierhttp://arxiv.org/abs/cond-mat/9510002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/147535
dc.subjectCondensed Matter
dc.titleTheory of random matrices with strong level confinement
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