Rank deficiency of Bernoulli random matrices for growing corank

Zeyan Song; Hanchao Wang

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arXiv · 2607.00495

Rank deficiency of Bernoulli random matrices for growing corank

Zeyan Song·Hanchao Wang

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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+o_n(1))^(kn).

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Zeyan Song, Hanchao Wang. 2026-07-01. Rank deficiency of Bernoulli random matrices for growing corank. https://arxiv.org/abs/2607.00495

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