On random matrices with large corank Hunter, Zach Kwan, Matthew Alan ; https://orcid.org/0000-0002-4003-7567 Sauermann, Lisa Sawhney, Mehtaab ddc:500 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). Oxford University Press 2026 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22147 https://research-explorer.ista.ac.at/download/22147/22151 Hunter Z, Kwan MA, Sauermann L, Sawhney M. On random matrices with large corank. <i>International Mathematics Research Notices</i>. 2026;2026(12). doi:<a href="https://doi.org/10.1093/imrn/rnag126">10.1093/imrn/rnag126</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1093/imrn/rnag126 info:eu-repo/semantics/altIdentifier/issn/1073-7928 info:eu-repo/semantics/altIdentifier/e-issn/1687-0247 info:eu-repo/semantics/altIdentifier/arxiv/2510.12933 info:eu-repo/semantics/openAccess