@article{22147,
  abstract     = {Let 1 ≤ k ≤ n and M be a random n × n matrix with independent uniformly random {±1}-entries. We
show that there exists an absolute constant c > 0 such that
P[rank(M) ≤ n − k] ≤ exp(−cnk).
This confirms a well-known prediction in the area, extending a result of Rudelson (who previously
proved this same result under the restriction k ≤ √n, via different methods).},
  author       = {Hunter, Zach and Kwan, Matthew Alan and Sauermann, Lisa and Sawhney, Mehtaab},
  issn         = {1687-0247},
  journal      = {International Mathematics Research Notices},
  number       = {12},
  publisher    = {Oxford University Press},
  title        = {{On random matrices with large corank}},
  doi          = {10.1093/imrn/rnag126},
  volume       = {2026},
  year         = {2026},
}