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arXiv · 2510.12933

On random matrices with large corank

Zach Hunter·Matthew Kwan·Lisa Sauermann·Mehtaab Sawhney
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Abstract

Let $1\le k\le n$ and $M$ be a random $n\times n$ matrix with independent uniformly random $\{\pm 1\}$-entries. We show that there exists an absolute constant $c > 0$ such that \[\mathbf{P}[\operatorname{rank}(M)\le n-k]\le \exp(-c nk).\]

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Zach Hunter, Matthew Kwan, Lisa Sauermann, Mehtaab Sawhney. 2025-10-14. On random matrices with large corank. https://arxiv.org/abs/2510.12933

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