Random doubly stochastic matrices: The circular law
Combinatorics
2014-03-28 v3 Probability
Abstract
Let be a matrix sampled uniformly from the set of doubly stochastic matrices of size . We show that the empirical spectral distribution of the normalized matrix converges almost surely to the circular law. This confirms a conjecture of Chatterjee, Diaconis and Sly.
Cite
@article{arxiv.1205.0843,
title = {Random doubly stochastic matrices: The circular law},
author = {Hoi H. Nguyen},
journal= {arXiv preprint arXiv:1205.0843},
year = {2014}
}
Comments
Published in at http://dx.doi.org/10.1214/13-AOP877 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)