On universality of bulk local regime of the deformed Gaussian unitary ensemble

T. Shcherbina

On universality of bulk local regime of the deformed Gaussian unitary ensemble

T. Shcherbina

Mathematics

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18 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 Ensemble (GUE) random matrix (independent of H_n⁽⁰⁾). Assuming that the Normalized Counting Measure of H_n⁽⁰⁾ converges weakly (in probability) to a nonrandom measure N ⁽⁰⁾ with a bounded support, we prove the universality of the local eigenvalue statistics in the bulk of the limiting spectrum of H_n.

Original language	English (US)
Pages (from-to)	396-433
Number of pages	38
Journal	Journal of Mathematical Physics, Analysis, Geometry
Volume	5
Issue number	4
State	Published - 2009

All Science Journal Classification (ASJC) codes

Analysis
Mathematical Physics
Geometry and Topology

Keywords

Gaussian unitary ensemble
Random matrices
Universality

Cite this

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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 Ensemble (GUE) random matrix (independent of Hn(0)). Assuming that the Normalized Counting Measure of Hn(0) converges weakly (in probability) to a nonrandom measure N (0) with a bounded support, we prove the universality of the local eigenvalue statistics in the bulk of the limiting spectrum of Hn.",

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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 Ensemble (GUE) random matrix (independent of Hn(0)). Assuming that the Normalized Counting Measure of Hn(0) converges weakly (in probability) to a nonrandom measure N (0) with a bounded support, we prove the universality of the local eigenvalue statistics in the bulk of the limiting spectrum of Hn.

KW - Gaussian unitary ensemble

KW - Random matrices

KW - Universality

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JO - Journal of Mathematical Physics, Analysis, Geometry

JF - Journal of Mathematical Physics, Analysis, Geometry

IS - 4

ER -

On universality of bulk local regime of the deformed Gaussian unitary ensemble

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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