Asymptotics of skew orthogonal polynomials

Abstract

Exact integral expressions of the skew orthogonal polynomials involved in Orthogonal (beta=1) and Symplectic (beta=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.

17 pages, Latex

References in corpus (3)

• Riemannian symmetric superspaces and their origin in random matrix theory
• Breakdown of universality in multi-cut matrix models
• Correlation functions of eigenvalues of multi-matrix models, and the limit of a time dependent matrix

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• Completing the picture for the smallest eigenvalue of real Wishart matrices
• Some properties of angular integrals
• Asymptotic expansion of beta matrix models in the multi-cut regime
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• Generalized Christoffel-Darboux formula for skew-orthogonal polynomials and random matrix theory
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• Surprising Pfaffian factorizations in Random Matrix Theory with Dyson index $\beta =2$
• Preserving Topology while Breaking Chirality: From Chiral Orthogonal to Anti-symmetric Hermitian Ensemble
• Bulk asymptotics of skew-orthogonal polynomials for quartic double well potential and universality in the matrix model