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1 November 2006 Random symmetric matrices are almost surely nonsingular
Kevin P. Costello, Terence Tao, Van Vu
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Duke Math. J. 135(2): 395-413 (1 November 2006). DOI: 10.1215/S0012-7094-06-13527-5

Abstract

Let Qn denote a random symmetric (n×n)-matrix, whose upper-diagonal entries are independent and identically distributed (i.i.d.) Bernoulli random variables (which take values 0 and 1 with probability 1/2). We prove that Qn is nonsingular 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

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Kevin P. Costello. Terence Tao. Van Vu. "Random symmetric matrices are almost surely nonsingular." Duke Math. J. 135 (2) 395 - 413, 1 November 2006. https://doi.org/10.1215/S0012-7094-06-13527-5

Information

Published: 1 November 2006
First available in Project Euclid: 17 October 2006

zbMATH: 1110.15020
MathSciNet: MR2267289
Digital Object Identifier: 10.1215/S0012-7094-06-13527-5

Subjects:
Primary: 15A52
Secondary: 05D40

Rights: Copyright © 2006 Duke University Press

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Vol.135 • No. 2 • 1 November 2006
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