Finite-Rank Complex Deformations of Random Band Matrices: Sigma-Model Approximation

被引：0

作者：

Shcherbina, Mariya ^{[1
]}

Shcherbina, Tatyana ^{[2
]}

机构：

[1] Natl Acad Sci Ukraine, B Verkin Inst Low Temp Phys & Engn, 47 Nauky Ave, UA-61103 Kharkiv, Ukraine

[2] Univ Wisconsin Madison, Dept Math, 480 Linkoln Dr, Madison, WI 53706 USA

来源：

JOURNAL OF MATHEMATICAL PHYSICS ANALYSIS GEOMETRY | 2023年 / 19卷 / 01期

关键词：

random band matrices; delocalized regime; complex defor-mation; sigma-model; supersymmetry; STATISTICS; POLES;

D O I：

10.15407/mag19.01.211

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the distribution of complex eigenvalues z1, ... , zN of random Hermitian N x N block band matrices with a complex deformation of a finite rank. Assuming that the width of the band W grows faster than v/N, we proved that the limiting density of sz1, ... , szN in a sigma-model approximation coincides with that for the Gaussian Unitary Ensemble. The method follows the techniques of [16].

引用

页码：211 / 246

页数：36

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