The singularity probability of a random symmetric matrix is exponentially small

Matthew Jenssen; Julian  Sahasrabudhe; Marcus  Michelen; Marcelo Campos

The singularity probability of a random symmetric matrix is exponentially small

Matthew Jenssen, Julian Sahasrabudhe, Marcus Michelen, Marcelo Campos

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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 \[ \PP( \det(A) = 0 ) \leq e^{-cn},\] where $c>0$ is an absolute constant, thereby resolving a long-standing conjecture.

Original language	English
Journal	Journal of the American Mathematical Society
Publication status	Accepted/In press - 22 Nov 2023

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title = "The singularity probability of a random symmetric matrix is exponentially small",

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 \[ \PP( \det(A) = 0 ) \leq e^{-cn},\] where $c>0$ is an absolute constant, thereby resolving a long-standing conjecture.",

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AU - Jenssen, Matthew

AU - Sahasrabudhe, Julian

AU - Michelen, Marcus

AU - Campos, Marcelo

PY - 2023/11/22

Y1 - 2023/11/22

N2 - 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 \[ \PP( \det(A) = 0 ) \leq e^{-cn},\] where $c>0$ is an absolute constant, thereby resolving a long-standing conjecture.

AB - 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 \[ \PP( \det(A) = 0 ) \leq e^{-cn},\] where $c>0$ is an absolute constant, thereby resolving a long-standing conjecture.

M3 - Article

SN - 0894-0347

JO - Journal of the American Mathematical Society

JF - Journal of the American Mathematical Society

ER -

The singularity probability of a random symmetric matrix is exponentially small

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