Linear statistics of the circular $\beta$-ensemble, Stein's method, and circular Dyson Brownian motion
Probability
2016-04-26 v3 Mathematical Physics
math.MP
Abstract
We study the linear statistics of the circular -ensemble with a Stein's method argument, where the exchangeable pair is generated through circular Dyson Brownian motion. This generalizes previous results obtained in such a way for the CUE and provides a novel approach for studying linear statistics of -ensembles. This approach allows studying simultaneously a collection of linear statistics whose number grows with the dimension of the ensemble. Also this approach requires estimating only low order moments of the linear statistics.
Keywords
Cite
@article{arxiv.1507.08670,
title = {Linear statistics of the circular $\beta$-ensemble, Stein's method, and circular Dyson Brownian motion},
author = {Christian Webb},
journal= {arXiv preprint arXiv:1507.08670},
year = {2016}
}