Rank deficiency of random matrices

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Electronic Communications in Probability Pub Date : 2021-03-03 DOI:10.1214/22-ecp455

Vishesh Jain, A. Sah, Mehtaab Sawhney

引用次数: 2

Abstract

Let $M_n$ be a random $n\times n$ matrix with i.i.d. $\text{Bernoulli}(1/2)$ entries. We show that for fixed $k\ge 1$, \[\lim_{n\to \infty}\frac{1}{n}\log_2\mathbb{P}[\text{corank }M_n\ge k] = -k.\]

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随机矩阵的秩亏

设$M_n$是具有i.i.d.$\text｛Bernoulli｝（1/2）$条目的随机$n\timesn$矩阵。我们证明了对于固定的$k\ge1$，\[\lim_｛n\to\infty｝\frac｛1｝｛n｝\log_2\mathbb｛P｝[\text｛corank｝M_n\gek]=-k

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Electronic Communications in Probability 工程技术-统计学与概率论

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Electronic Communications in Probability (ECP) publishes short research articles in probability theory. Its sister journal, the Electronic Journal of Probability (EJP), publishes full-length articles in probability theory. Short papers, those less than 12 pages, should be submitted to ECP first. EJP and ECP share the same editorial board, but with different Editors in Chief.