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 2015Show all

2 papers · 1 filter

math.PR2015★ 42 cited

Size biased couplings and the spectral gap for random regular graphs

Nicholas A. Cook, Larry Goldstein, Tobias Johnson

Let $λ$ be the second largest eigenvalue in absolute value of a uniform random $d$ -regular graph on $n$ vertices. It was famously conjectured by Alon and proved by Friedman that if…

math.PR2015★ 8 cited

The circular law for random regular digraphs with random edge weights

Nicholas A. Cook

We consider random $n \times n$ matrices of the form $Y_{n} = \frac{1}{d} A_{n} \circ X_{n}$ , where $A_{n}$ is the adjacency matrix of a uniform random $d$ -regular directed graph on $n$ ve…