Non-asymptotic Theory of Random Matrices: Extreme Singular Values

被引：0

作者：

Rudelson, Mark ^{[1
]}

Vershynin, Roman ^{[2
]}

机构：

[1] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

来源：

PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS, VOL III: INVITED LECTURES | 2010年

关键词：

Random matrices; singular values; hard edge; Littlewood-Offord problem; small ball probability; LITTLEWOOD-OFFORD PROBLEM; RESTRICTED ISOMETRY PROPERTY; LARGEST EIGENVALUE; GAUSSIAN-PROCESSES; SMALLEST EIGENVALUE; CONDITION NUMBERS; INEQUALITIES; EMBEDDINGS; BERNOULLI; LIMIT;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to information theory operate with random matrices in fixed dimensions. This survey addresses the non-asymptotic theory of extreme singular values of random matrices with independent entries. We focus on recently developed geometric methods for estimating the hard edge of random matrices (the smallest singular value).

引用

页码：1576 / 1602

页数：27

共 97 条

[1]

Adamczak R, 2010, J AM MATH SOC, V23, P535

[2]

[Anonymous], SPRINGER SERIES STAT

[3]

[Anonymous], 2002, Proceedings of the International Congress of Mathematicians

[4] Polynomial bounds for large Bernoulli sections of lN1 [J].