On Universality of Bulk Local Regime of the Deformed Gaussian Unitary Ensemble

2008/04/14 by Tatyana Shcherbina, T. Shcherbina, Shcherbina, T. · 1 citation
Mathematics · Physics and Astronomy · #15A52 #15A57 #Advanced Algebra and Geometry #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Random Matrices and Applications #math-ph #math.MP #msc:15A52 #msc:15A57

paper · pdf · doi:10.48550/arxiv.0804.2116

37 pages, 1 figure

arxiv created 2008/04/14 · openalex publication_date 2008/04/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the deformed Gaussian Ensemble H_n=M_n+H⁽⁰⁾_n in which H_n⁽⁰⁾ is a diagonal Hermitian matrix and M_n is the Gaussian Unitary Ensemble (GUE) random matrix. Assuming that the Normalized Counting Measure of H_n⁽⁰⁾ (both non-random and random) converges weakly to a measure N⁽⁰⁾ with a bounded support we prove universality of the local eigenvalue statistics in the bulk of the limiting spectrum of H_n.

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