Year: 2026
Type: preprint
Abstract: Let $G_{n,d}$ be a uniformly random simple $d$-regular graph on $n$ vertices, and let $A_n$ be its adjacency matrix. For every fixed $λ\in(0,1/2)$, we prove that for any $λ(n-1)\le d\le(1-λ)(n-1)$, $\mathbb P(A_n\text{ is singular})\le e^{-cn}$, where $c>0$ depends only on $λ$, and $n$ is sufficiently large with $nd$ even.
Source: arXiv (Cornell University)
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Strong
OpenAlex ID: W7220957238