2005/09/14 by L. А. Pastur, Leonid Pastur, Pastur, Leonid
Mathematics · Physics and Astronomy · #11C08 #11C20 #15A52 #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.MP #msc:11C08 #msc:11C20 #msc:15A52
paper · pdf · doi:10.48550/arxiv.math-ph/0509029
arxiv created 2005/09/14 · openalex publication_date 2005/09/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We 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.