From Random Matrices to Quasiperiodic Jacobi Matrices via Orthogonal Polynomials

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dc.creatorPastur, Leonid
dc.date2005-09-14
dc.date.accessioned2026-07-07T04:32:20Z
dc.date.available2026-07-07T04:32:20Z
dc.descriptionWe present an informal review of results on asymptotics of orthogonal polynomials, stressing their spectral aspects and similarity in two cases considered. They are polynomials orthonormal on a finite union of disjoint intervals with respect to the Szego weight and polynomials orthonormal on R with respect to varying weights and having the same union of intervals as the set of oscillations of asymptotics. In both cases we construct double infinite Jacobi matrices with generically quasiperiodic coefficients and show that each of them is an isospectral deformation of another. Related results on asymptotic eigenvalue distribution of a class of random matrices of large size are also shortly discussed.
dc.identifierhttps://arxiv.org/abs/math-ph/0509029
dc.identifierhttp://arxiv.org/abs/math-ph/0509029
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58156
dc.subjectMathematical Physics
dc.subject15A52; 11C08; 11C20
dc.titleFrom Random Matrices to Quasiperiodic Jacobi Matrices via Orthogonal Polynomials
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