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Singularity of random Bernoulli matrices (1812.09016v4)
Published 21 Dec 2018 in math.PR and math.CO
Abstract: 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.
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