On Universality of Local Edge Regime for the Deformed Gaussian Unitary Ensemble

T. Shcherbina

doi:10.1007/s10955-011-0196-9

On Universality of Local Edge Regime for the Deformed Gaussian Unitary Ensemble

T. Shcherbina

Mathematics

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20 Scopus citations

Abstract

We consider the deformed Gaussian ensemble H_n=H_n ⁽⁰⁾ + M_n in which H_n ⁽⁰⁾ is a hermitian matrix (possibly random) and M_n is the Gaussian unitary random matrix (GUE) independent of H_n ⁽⁰⁾. Assuming that the Normalized Counting Measure of H_n ⁽⁰⁾ converges weakly (in probability if random) to a non-random measure N⁽⁰⁾ with a bounded support and assuming some conditions on the convergence rate, we prove the universality of the local eigenvalue statistics near the edge of the limiting spectrum of H_n.

Original language	English (US)
Pages (from-to)	455-481
Number of pages	27
Journal	Journal of Statistical Physics
Volume	143
Issue number	3
DOIs	https://doi.org/10.1007/s10955-011-0196-9
State	Published - May 2011

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

Airy kernel
Deformed GUE
Edge universality
Random matrices

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10.1007/s10955-011-0196-9

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abstract = "We consider the deformed Gaussian ensemble Hn=Hn (0) + Mn in which Hn (0) is a hermitian matrix (possibly random) and Mn is the Gaussian unitary random matrix (GUE) independent of Hn (0). Assuming that the Normalized Counting Measure of Hn (0) converges weakly (in probability if random) to a non-random measure N(0) with a bounded support and assuming some conditions on the convergence rate, we prove the universality of the local eigenvalue statistics near the edge of the limiting spectrum of Hn.",

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N2 - We consider the deformed Gaussian ensemble Hn=Hn (0) + Mn in which Hn (0) is a hermitian matrix (possibly random) and Mn is the Gaussian unitary random matrix (GUE) independent of Hn (0). Assuming that the Normalized Counting Measure of Hn (0) converges weakly (in probability if random) to a non-random measure N(0) with a bounded support and assuming some conditions on the convergence rate, we prove the universality of the local eigenvalue statistics near the edge of the limiting spectrum of Hn.

AB - We consider the deformed Gaussian ensemble Hn=Hn (0) + Mn in which Hn (0) is a hermitian matrix (possibly random) and Mn is the Gaussian unitary random matrix (GUE) independent of Hn (0). Assuming that the Normalized Counting Measure of Hn (0) converges weakly (in probability if random) to a non-random measure N(0) with a bounded support and assuming some conditions on the convergence rate, we prove the universality of the local eigenvalue statistics near the edge of the limiting spectrum of Hn.

KW - Airy kernel

KW - Deformed GUE

KW - Edge universality

KW - Random matrices

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On Universality of Local Edge Regime for the Deformed Gaussian Unitary Ensemble

Abstract

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Keywords

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