Asymptotics of skew orthogonal polynomials

2000/12/04 by B Eynard, B. Eynard
Mathematics · Physics and Astronomy · #Classical orthogonal polynomials #Discrete orthogonal polynomials #Gegenbauer polynomials #Geometry and complex manifolds #Hahn polynomials #Jacobi polynomials #Mathematical functions and polynomials #Orthogonal polynomials #Random Matrices and Applications #Skew #Wilson polynomials #cond-mat.mes-hall #math-ph #math.MP

paper · pdf · doi:10.1088/0305-4470/34/37/312

published as J. Phys. A. 34 2001 7591-7605 · 17 pages, Latex

arxiv created 2000/12/04 · openalex publication_date 2001/09/10 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

Abstract

Exact integral expressions of the skew orthogonal polynomials involved in orthogonal (β = 1) and symplectic (β = 4) random matrix ensembles are obtained: the (even rank) skew orthogonal polynomials are average characteristic polynomials of random matrices. From there, asymptotics of the skew orthogonal polynomials are derived.

Citations

• Random Matrix Theories in Quantum Physics: Common Concepts
• Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles
• Breakdown of universality in multi-cut matrix models
• Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws