Publications [#350407] of Nicholas A Cook

Papers Published

1. Cook, N, The Circular Law for random regular digraphs, Annales De L Institut Henri Poincare B Probability and Statistics, vol. 55 no. 4 (January, 2019), pp. 2111-2167 [doi]
   (last updated on 2026/01/15)

   Abstract:
   Let log^C n ≤ d ≤ n/2 for a sufficiently large constant C > 0 and let An denote the adjacency matrix of a uniform random d-regular directed graph on n vertices. We prove that as n tends to infinity, the empirical spectral distribution of An, suitably rescaled, is governed by the Circular Law. A key step is to obtain quantitative lower tail bounds for the smallest singular value of additive perturbations of An