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arXiv · 2105.11384

The singularity probability of a random symmetric matrix is exponentially small

Marcelo Campos·Matthew Jenssen·Marcus Michelen·Julian Sahasrabudhe
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Abstract

Let $A$ be drawn uniformly at random from the set of all $n\times n$ symmetric matrices with entries in $\{-1,1\}$. We show that \[ \mathbb{P}( \det(A) = 0 ) \leq e^{-cn},\] where $c>0$ is an absolute constant, thereby resolving a well-known conjecture.

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Marcelo Campos, Matthew Jenssen, Marcus Michelen, Julian Sahasrabudhe. 2021-05-24. The singularity probability of a random symmetric matrix is exponentially small. https://arxiv.org/abs/2105.11384

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