Year: 2023
Type: preprint
Abstract: In this note we show that the singular probability of the adjacency matrix of a random $d$-regular graph on $n$ vertices, where $d$ is fixed and $n \to \infty$, is bounded by $n^{-1/3+o(1)}$. This improves a recent bound by Huang. Our method is based on the study of the singularity problem modulo a prime together with an inverse-type result on the decay of the characteristic function. The latter is related to the inverse Kneser's problem in combinatorics.
Source: arXiv (Cornell University)
Authors: Nguyen, Hoi H., Pan, Amanda
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4385848511