Gaussian Beta Ensembles at High Temperature: Eigenvalue Fluctuations and Bulk Statistics |
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| Authors: | Fumihiko Nakano Khanh Duy Trinh |
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| Affiliation: | 1.Department of Mathematics,Gakushuin University,Tokyo,Japan;2.Institute of Mathematics for Industry,Kyushu University,Fukuoka,Japan;3.Research Alliance Center for Mathematical Sciences,Tohoku University,Sendai,Japan |
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| Abstract: | We study the limiting behavior of Gaussian beta ensembles in the regime where (beta n = const) as (n rightarrow 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 Benaych-Georges and Péché (J Stat Phys 161(3):633–656, 2015) with the explicit form of the intensity measure. |
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