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arXiv · 2308.06461

A note on the singularity probability of random directed $d$-regular graphs

Hoi H. Nguyen·Amanda Pan
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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.

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Hoi H. Nguyen, Amanda Pan. 2023-08-12. A note on the singularity probability of random directed $d$-regular graphs. https://arxiv.org/abs/2308.06461

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