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- W2949209719 abstract "We prove that the (non-symmetric) adjacency matrix of a uniform random $d$-regular directed graph on $n$ vertices is asymptotically almost surely invertible, assuming $min(d,n-d)ge Clog^2n$ for a sufficiently large constant $C>0$. The proof makes use of a coupling of random regular digraphs formed by shuffling the neighborhood of a pair of vertices, as well as concentration results for the distribution of edges recently obtained by the author (arXiv:1410.5595). We also apply our general approach to prove a.a.s. invertibility of Hadamard products $Sigmacirc Xi$, where $Xi$ is a matrix of iid uniform $pm1$ signs, and $Sigma$ is a 0/1 matrix whose associated digraph satisfies certain expansion properties." @default.
- W2949209719 created "2019-06-27" @default.
- W2949209719 creator A5067825540 @default.
- W2949209719 date "2014-11-02" @default.
- W2949209719 modified "2023-09-23" @default.
- W2949209719 title "On the singularity of adjacency matrices for random regular digraphs" @default.
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