On random matrices with large corank
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866915555525525504 |
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| author | Hunter, Zach Kwan, Matthew Sauermann, Lisa Sawhney, Mehtaab |
| author_facet | Hunter, Zach Kwan, Matthew Sauermann, Lisa Sawhney, Mehtaab |
| contents | 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 \[\mathbf{P}[\operatorname{rank}(M)\le n-k]\le \exp(-c nk).\] |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12933 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On random matrices with large corank Hunter, Zach Kwan, Matthew Sauermann, Lisa Sawhney, Mehtaab Probability 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 \[\mathbf{P}[\operatorname{rank}(M)\le n-k]\le \exp(-c nk).\] |
| title | On random matrices with large corank |
| topic | Probability |
| url | https://arxiv.org/abs/2510.12933 |