The Circular Law for random regular digraphs

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

Duke Scholars

Author Nicholas A Cook Mathematics