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The singularity probability of a random symmetric matrix is exponentially small (2105.11384v2)
Published 24 May 2021 in math.PR and math.CO
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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