The Circular Law for random regular digraphs

Journal Article

© Association des Publications de l’Institut Henri Poincaré, 2019 Let logC 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

Full Text

Duke Authors

Cited Authors

  • Cook, N

Published Date

  • January 1, 2019

Published In

Volume / Issue

  • 55 / 4

Start / End Page

  • 2111 - 2167

International Standard Serial Number (ISSN)

  • 0246-0203

Digital Object Identifier (DOI)

  • 10.1214/18-AIHP943

Citation Source

  • Scopus