Singularity of random Bernoulli matrices

  title={Singularity of random Bernoulli matrices},
  author={Konstantin E. Tikhomirov},
  journal={arXiv: Probability},
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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