Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invertibility of adjacency matrices for random d-regular directed graphs   Let $d\geq 3$ be a fixed integer, and a prime number $p$ such that
$\gcd(p,d)=1$. Let $A$ be the adjacency matrix of a random $d$-regular directed
graph on $n$ vertices. We show that as a random matrix in ${\mathbb F}_p$,
\begin{equation} {\mathbb P}(\text{$A$ is singular in ${\mathbb F}_p$})\leq
\frac{1+{\mathrm{o}}(1)}{p-1}, \end{equation} as $n$ goes to infinity. As a
consequence, as a random matrix in $\mathbb R$, \begin{equation} {\mathbb
P}(\text{$A$ is singular in $\mathbb R$})={\mathrm{o}}(1) \end{equation} as $n$
goes to infinity. This answers an open problem by Frieze [12] and Vu [29,30],
for random $d$-regular bipartite graphs. The proof combines a local central
limit theorem and a large deviation estimate.

35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph