On Universality for Orthogonal Ensembles of Random Matrices

2007/01/31 by Mariya Shcherbina, M. Shcherbina · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Random Matrices and Applications #math-ph #math.MP #msc:15A52 #msc:15A57

paper · pdf · doi:10.1007/s00220-008-0648-5

23 pages

arxiv created 2007/11/12 · openalex publication_date 2008/10/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

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.

Citations

• 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

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