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

collaborators

Showing 2017Show all

2 papers · 1 filter

math.PR2017

Circular law for the sum of random permutation matrices

Anirban Basak, Nicholas Cook, Ofer Zeitouni

Let $P_{n}^{1}, \dots, P_{n}^{d}$ be $n \times n$ permutation matrices drawn independently and uniformly at random, and set $S_{n}^{d} := \sum_{ℓ = 1}^{d} P_{n}^{ℓ}$ . We show that if $\log^{12}n/(\l…

math.PR2017

The circular law for random regular digraphs

Nicholas A. Cook

Let $lo g^{C} n \leq d \leq n /2$ for a sufficiently large constant $C > 0$ and let $A_{n}$ denote the adjacency matrix of a uniform random $d$ -regular directed graph on $n$ vertices. We prove…