Edge Universality for Orthogonal Ensembles of Random Matrices

Abstract

We prove edge universality of local eigenvalue statistics for orthogonal invariant matrix models with real analytic potentials and one interval limiting spectrum. Our starting point is the result of \cite{S:08} on the representation of the reproducing matrix kernels of orthogonal ensembles in terms of scalar reproducing kernel of corresponding unitary ensemble.

14 pages

References in corpus (6)

• Level-Spacing Distributions and the Airy Kernel
• 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
• Universality for orthogonal and symplectic Laguerre-type ensembles
• On Universality for Orthogonal Ensembles of Random Matrices

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