The circular law for random regular digraphs with random edge weights

Journal Article

© 2017 World Scientific Publishing Company. We consider random n × n matrices of the form Yn = 1 dAn Xn, where An is the adjacency matrix of a uniform random d-regular directed graph on n vertices, with d = ?pn? for some fixed p (0, 1), and Xn is an n × n matrix of i.i.d. centered random variables with unit variance and finite (4 + ?)th moment (here denotes the matrix Hadamard product). We show that as n →∞, the empirical spectral distribution of Yn converges weakly in probability to the normalized Lebesgue measure on the unit disk.

Full Text

Duke Authors

Cited Authors

  • Cook, N

Published Date

  • July 1, 2017

Published In

Volume / Issue

  • 6 / 3

Electronic International Standard Serial Number (EISSN)

  • 2010-3271

International Standard Serial Number (ISSN)

  • 2010-3263

Digital Object Identifier (DOI)

  • 10.1142/S2010326317500125

Citation Source

  • Scopus