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1 April 2021 On the singularity of random symmetric matrices
Marcelo Campos, Letícia Mattos, Robert Morris, Natasha Morrison
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Duke Math. J. 170(5): 881-907 (1 April 2021). DOI: 10.1215/00127094-2020-0054

Abstract

A well-known conjecture states that a random symmetric n×n matrix with entries in {1,1} is singular with probability Θ(n22n). We prove that the probability of this event is at most exp(Ω(n)), improving the best-known bound of exp(Ω(n14logn)), which was obtained recently by Ferber and Jain. The main new ingredient is an inverse Littlewood–Offord theorem in Zpn that applies under very mild conditions, whose statement is inspired by the method of hypergraph containers.

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Marcelo Campos. Letícia Mattos. Robert Morris. Natasha Morrison. "On the singularity of random symmetric matrices." Duke Math. J. 170 (5) 881 - 907, 1 April 2021. https://doi.org/10.1215/00127094-2020-0054

Information

Received: 27 April 2019; Revised: 9 April 2020; Published: 1 April 2021
First available in Project Euclid: 18 March 2021

Digital Object Identifier: 10.1215/00127094-2020-0054

Subjects:
Primary: 60B20
Secondary: 05D40, 15B52

Rights: Copyright © 2021 Duke University Press

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Vol.170 • No. 5 • 1 April 2021
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