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Singularity of random Bernoulli matrices
Annals of Mathematics ( IF 5.7 ) Pub Date : 2020-01-01 , DOI: 10.4007/annals.2020.191.2.6
Konstantin Tikhomirov 1
Affiliation  

For each $n$, let $M_n$ be an $n\times n$ random matrix with independent $\pm 1$ entries. We show that ${\mathbb P}\{\mbox{$M_n$ is singular}\}=(1/2+o_n(1))^n$, which settles an old problem. Some generalizations are considered.

中文翻译:

随机伯努利矩阵的奇异性

对于每个 $n$,让 $M_n$ 是一个 $n\times n$ 随机矩阵,其中包含独立的 $\pm 1$ 个条目。我们证明 ${\mathbb P}\{\mbox{$M_n$ 是单数}\}=(1/2+o_n(1))^n$,这解决了一个老问题。考虑了一些概括。
更新日期:2020-01-01
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