Circular law for random block band matrices with genuinely sublinear bandwidth

被引：2

作者：

Jain, Vishesh ^{[1
]}

Jana, Indrajit ^{[2
]}

Luh, Kyle ^{[3
]}

O'Rourke, Sean ^{[3
]}

机构：

[1] Stanford Univ, Dept Stat, Stanford, CA 94305 USA

[2] Indian Inst Technol, Bhubaneswar, India

[3] Univ Colorado, Dept Math, Boulder, CO 80309 USA

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2021年 / 62卷 / 08期

关键词：

SCALING PROPERTIES; FLUCTUATIONS; UNIVERSALITY; EIGENVALUES; DELOCALIZATION; DISTRIBUTIONS; LOCALIZATION; PRODUCTS; SPECTRUM; BOUNDS;

D O I：

10.1063/5.0042590

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We prove the circular law for a class of non-Hermitian random block band matrices with genuinely sublinear bandwidth. Namely, we show that there exists tau is an element of (0, 1) so that if the bandwidth of the matrix X is at least n(1-tau) and the nonzero entries are iid random variables with mean zero and slightly more than four finite moments, then the limiting empirical eigenvalue distribution of X, when properly normalized, converges in probability to the uniform distribution on the unit disk in the complex plane. The key technical result is a least singular value bound for shifted random band block matrices with genuinely sublinear bandwidth, which improves on a result of Cook [Ann. Probab. 46, 3442 (2018)] in the band matrix setting.

引用

页数：27

共 87 条

[1] Circular law for random matrices with exchangeable entries [J].