Circular law for the sum of random permutation matrices

Journal Article

© 2018, University of Washington. All rights reserved. Let Pn1, …, Pnd be n × n permutation matrices drawn independently and uniformly at random, and set Snd := ∑ℓ-1d Pnℓ. We show that if log12n/(log log n)4 ≤ d = O(n), then the empirical spectral distribution of Snd/√d converges weakly to the circular law in probability as n → ∞.

Full Text

Duke Authors

Cited Authors

  • Basak, A; Cook, N; Zeitouni, O

Published Date

  • January 1, 2018

Published In

Volume / Issue

  • 23 /

Electronic International Standard Serial Number (EISSN)

  • 1083-6489

Digital Object Identifier (DOI)

  • 10.1214/18-EJP162

Citation Source

  • Scopus