Rank deficiency of Bernoulli random matrices for growing corank
Abstract
Let A be an n x n Bernoulli random matrix whose entries are i.i.d. Bernoulli(p) random variables. In this paper, we determine the probability that the corank of A is at least k when k is of order O(sqrt(log n)): P(corank A >= k) = (1-p+on(1))(kn).
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