The Smallest Singular Value of a Shifted Random Matrix

被引：0

作者：

Dong, Xiaoyu ^{[1
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48104 USA

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2023年 / 36卷 / 04期

关键词：

Random matrices; Smallest singular value; Smoothed analysis; The Littlewood-Offord problem; CONDITION NUMBERS; SMOOTHED ANALYSIS; INVERTIBILITY;

D O I：

10.1007/s10959-023-01255-8

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let R-n be an n x n random matrix with i.i.d. subgaussian entries. Let M be an n x n deterministic matrix with norm ||M ||= n(?) where 1/2 < ? < 1. The goal of this paper is to give a general estimate of the smallest singular value of the sum R-n + M, which improves an earlier result of Tao and Vu.

引用

页码：2448 / 2475

页数：28

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