Singularity of random Bernoulli matrices

By Konstantin E. Tikhomirov. Annals of Mathematics, 2018

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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.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/124098f7b462bb7dd2f23f7e39c9b9e79925daba