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• W2942127735 abstract "A well-known conjecture states that a random symmetric $n times n$ matrix with entries in ${-1,1}$ is singular with probability $Thetabig( n^2 2^{-n} big)$. In this paper we prove that the probability of this event is at most $expbig( - Omega( sqrt{n} ) big)$, improving the best known bound of $expbig( - Omega( n^{1/4} sqrt{log n} ) big)$, which was obtained recently by Ferber and Jain. The main new ingredient is an inverse Littlewood-Offord theorem in $mathbb{Z}_p^n$ that applies under very mild conditions, whose statement is inspired by the method of hypergraph containers." @default.
• W2942127735 created "2019-05-03" @default.
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• W2942127735 date "2019-04-25" @default.
• W2942127735 modified "2023-09-27" @default.
• W2942127735 title "On the singularity of random symmetric matrices" @default.
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