Singularity of random Bernoulli matrices
Abstract
For each $n$, let $M_n$ be an $n\times n$ random matrix with independent $\pm 1$ entries. We show that ${\mathbb P}\{\mbox{$M_n$ is singular}\}=(1/2+o_n(1))^n$, which settles an old problem. Some generalizations are considered.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2018
- DOI:
- 10.48550/arXiv.1812.09016
- arXiv:
- arXiv:1812.09016
- Bibcode:
- 2018arXiv181209016T
- Keywords:
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- Mathematics - Probability;
- Mathematics - Combinatorics
- E-Print:
- Rearranged auxiliary statements, added a detailed description of the proof