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BIRS Workshop Lecture Videos

Singularity of 0/1 random Bernoulli matrices Litvak, Alexander


Let $M$ be a random $n\times n$ matrix with independent 0/1 random entries taking value 1 with probability $0 < p=p(n) < 1$. We provide sharp bounds on the probability that $M$ is singular for $C(\ln n)/n\leq p\leq c$, where $C, c$ are absolute positive constants. Roughly speaking, we show that this probability is essentially equal to the probability that $M$ has either zero row or zero column. Joint work with Konstantin Tikhomirov.

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