Let $A$ be drawn uniformly at random from the set of all $nn$
symmetric matrices with entries in $\-1,1\$. We show that \ P(
\det(A) = 0 ) e^-cn,\ where $c>0$ is an absolute constant, thereby
resolving a well-known conjecture.
Beschreibung
[2105.11384] The singularity probability of a random symmetric matrix is exponentially small
%0 Journal Article
%1 campos2021singularity
%A Campos, Marcelo
%A Jenssen, Matthew
%A Michelen, Marcus
%A Sahasrabudhe, Julian
%D 2021
%K mathematics probability randomized
%T The singularity probability of a random symmetric matrix is
exponentially small
%U http://arxiv.org/abs/2105.11384
%X Let $A$ be drawn uniformly at random from the set of all $nn$
symmetric matrices with entries in $\-1,1\$. We show that \ P(
\det(A) = 0 ) e^-cn,\ where $c>0$ is an absolute constant, thereby
resolving a well-known conjecture.
@article{campos2021singularity,
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.},
added-at = {2021-05-26T10:55:05.000+0200},
author = {Campos, Marcelo and Jenssen, Matthew and Michelen, Marcus and Sahasrabudhe, Julian},
biburl = {https://www.bibsonomy.org/bibtex/2ab2eb422c249fce8d655c271d4ef7d02/kirk86},
description = {[2105.11384] The singularity probability of a random symmetric matrix is exponentially small},
interhash = {166cacf6a582940383cd443356f1b49d},
intrahash = {ab2eb422c249fce8d655c271d4ef7d02},
keywords = {mathematics probability randomized},
note = {cite arxiv:2105.11384Comment: 48 pages},
timestamp = {2021-05-26T10:55:05.000+0200},
title = {The singularity probability of a random symmetric matrix is
exponentially small},
url = {http://arxiv.org/abs/2105.11384},
year = 2021
}