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. Non UBC Unreviewed Author affiliation: University of Alberta Faculty