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1 December 2021 Invertibility of adjacency matrices for random d-regular graphs
Jiaoyang Huang
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Duke Math. J. 170(18): 3977-4032 (1 December 2021). DOI: 10.1215/00127094-2021-0006

Abstract

Let d3 be a fixed integer, and let A be the adjacency matrix of a random d-regular directed or undirected graph on n vertices. We show that there exists a constant d>0 such that

P(Ais singular inR)nd,

for n sufficiently large. This answers an open problem by Frieze and Vu. The key idea is to study the singularity probability over a finite field Fp. The proof combines a local central limit theorem and a large deviation estimate.

Citation

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Jiaoyang Huang. "Invertibility of adjacency matrices for random d-regular graphs." Duke Math. J. 170 (18) 3977 - 4032, 1 December 2021. https://doi.org/10.1215/00127094-2021-0006

Information

Received: 1 January 2019; Revised: 13 January 2021; Published: 1 December 2021
First available in Project Euclid: 18 November 2021

Digital Object Identifier: 10.1215/00127094-2021-0006

Subjects:
Primary: 15B52
Secondary: 05C80 , 15B33

Keywords: random d-regular graph , random matrices , singularity problem

Rights: Copyright © 2021 Duke University Press

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Vol.170 • No. 18 • 1 December 2021
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