On Universality for Orthogonal Ensembles of Random Matrices

Abstract

We prove universality of local eigenvalue statistics in the bulk of the spectrum for orthogonal invariant matrix models with real analytic potentials with one interval limiting spectrum. Our starting point is the Tracy-Widom formula for the matrix reproducing kernel. The key idea of the proof is to represent the differentiation operator matrix written in the basis of orthogonal polynomials as a product of a positive Toeplitz matrix and a two diagonal skew symmetric Toeplitz matrix.

23 pages

References in corpus (5)

• 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
• Bulk Universality and Related Properties of Hermitian Matrix Models
• On the edge universality of the local eigenvalue statistics of matrix models
• Universality for orthogonal and symplectic Laguerre-type ensembles

Cited by in corpus (7)

• Combinatorics of dispersionless integrable systems and universality in random matrix theory
• Orthogonal and symplectic matrix models: universality and other properties
• Change of variables as a method to study general $\beta$-models: bulk universality
• On Random Matrix Averages Involving Half-Integer Powers of GOE Characteristic Polynomials
• The rank 1 real Wishart spiked model
• Edge Universality for Orthogonal Ensembles of Random Matrices
• A Riemann-Hilbert Approach to Skew-Orthogonal Polynomials of Symplectic Type