Gaussian beta ensembles at high temperature: eigenvalue fluctuations and bulk statistics
Probability
2017-09-25 v2
Abstract
We study the limiting behavior of Gaussian beta ensembles in the regime where as . The results are (1) Gaussian fluctuations for linear statistics of the eigenvalues, and (2) Poisson convergence of the bulk statistics. (2) is an alternative proof of the result by F.~Benaych-Georges and S.~P\'ech\'e (2015) with the explicit form of the intensity measure.
Cite
@article{arxiv.1611.09476,
title = {Gaussian beta ensembles at high temperature: eigenvalue fluctuations and bulk statistics},
author = {Trinh Khanh Duy and Fumihiko Nakano},
journal= {arXiv preprint arXiv:1611.09476},
year = {2017}
}
Comments
We corrected the proof of the local law