Generalized Christoffel-Darboux formula for skew-orthogonal polynomials and random matrix theory

Abstract

We obtain generalized Christoffel-Darboux (GCD) formula for skew-orthogonal polynomials (SOP). Using this, we present an alternative derivation of the level density and two-point function for Gaussian orthogonal ensembles (GOE) and Gaussian symplectic ensembles (GSE) of random matrices.

8 pages

References in corpus (6)

• On Orthogonal and Symplectic Matrix Ensembles
• Correlation Functions, Cluster Functions and Spacing Distributions for Random Matrices
• Universality at the edge of the spectrum for unitary, orthogonal and symplectic ensembles of random matrices
• Classical skew orthogonal polynomials and random matrices
• Asymptotics of skew orthogonal polynomials
• A concise expression for the ODE's of orthogonal polynomials

Cited by in corpus (5)

• Skew-orthogonal polynomials, differential systems and random matrix theory
• Generalized Christoffel-Darboux formula for classical skew-orthogonal polynomials
• A Riemann-Hilbert Approach to Skew-Orthogonal Polynomials of Symplectic Type
• Skew-orthogonal polynomials: the quartic case
• Bulk asymptotics of skew-orthogonal polynomials for quartic double well potential and universality in the matrix model