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.
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收藏
页码：2448 / 2475
页数：28
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