Random symmetric matrices are almost surely non-singular

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dc.creatorCostello, Kevin
dc.creatorTao, Terence
dc.creatorVu, Van
dc.date2005-05-09
dc.date.accessioned2026-07-07T05:19:44Z
dc.date.available2026-07-07T05:19:44Z
dc.descriptionLet $Q_n$ denote a random symmetric $n$ by $n$ matrix, whose upper diagonal entries are i.i.d. Bernoulli random variables (which take values 0 and 1 with probability 1/2). We prove that $Q_n$ is non-singular with probability $1-O(n^{-1/8+δ})$ for any fixed $δ> 0$. The proof uses a quadratic version of Littlewood-Offord type results concerning the concentration functions of random variables and can be extended for more general models of random matrices.
dc.description16 pages, no figures, submitted, Duke Math J
dc.identifierhttps://arxiv.org/abs/math/0505156
dc.identifierhttp://arxiv.org/abs/math/0505156
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75125
dc.subjectProbability
dc.subject15A52
dc.titleRandom symmetric matrices are almost surely non-singular
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