Gaussian beta ensembles at high temperature: eigenvalue fluctuations and bulk statistics

Trinh Khanh Duy; Fumihiko Nakano

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arXiv · 1611.09476

Gaussian beta ensembles at high temperature: eigenvalue fluctuations and bulk statistics

Trinh Khanh Duy·Fumihiko Nakano

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Abstract

We study the limiting behavior of Gaussian beta ensembles in the regime where $\beta n = const$ as $n \to \infty$. 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.

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Trinh Khanh Duy, Fumihiko Nakano. 2016-11-29. Gaussian beta ensembles at high temperature: eigenvalue fluctuations and bulk statistics. https://arxiv.org/abs/1611.09476

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