Nicholas A. Cook

activity

20142025

most citedSize biased couplings and the spectral gap for random regular graphs

42 citations · 103 across the 13 of their papers we have counts for

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Showing 2014Show all

3 papers · 1 filter

math.PR2014★ 5 cited

On the singularity of adjacency matrices for random regular digraphs

Nicholas A. Cook

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)\…

math.CO2014

Discrepancy properties for random regular digraphs

Nicholas A. Cook

For the uniform random regular directed graph we prove concentration inequalities for (1) codegrees and (2) the number of edges passing from one set of vertices to another. As a co…

math.PR2014★ 2 cited

Dense random regular digraphs: singularity of the adjacency matrix

Nicholas A. Cook

Fix $c \in (0, 1)$ and let $Γ$ be a $⌊ c n ⌋$ -regular digraph on $n$ vertices drawn uniformly at random. We prove that when $n$ is large, the (non-symmetric) adjacency mat…