Rank deficiency of Bernoulli random matrices for growing corank

Zeyan Song; Hanchao Wang

Rank deficiency of Bernoulli random matrices for growing corank

Probability 2026-07-01 v1

Authors: Zeyan Song , Hanchao Wang

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).

Keywords

random matrices Bernoulli matrices rank deficiency corank singularity probability

Cite

@article{arxiv.2607.00495,
  title  = {Rank deficiency of Bernoulli random matrices for growing corank},
  author = {Zeyan Song and Hanchao Wang},
  journal= {arXiv preprint arXiv:2607.00495},
  year   = {2026}
}