Gaussian Beta Ensembles at High Temperature: Eigenvalue Fluctuations and Bulk Statistics

Fumihiko Nakano; Khanh Duy Trinh

doi:10.1007/s10955-018-2131-9

Gaussian Beta Ensembles at High Temperature: Eigenvalue Fluctuations and Bulk Statistics

Fumihiko Nakano, Khanh Duy Trinh^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

Abstract

We study the limiting behavior of Gaussian beta ensembles in the regime where βn= const as n→ ∞. 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.

Original language	English
Pages (from-to)	295-321
Number of pages	27
Journal	Journal of Statistical Physics
Volume	173
Issue number	2
DOIs	https://doi.org/10.1007/s10955-018-2131-9
Publication status	Published - 2018 Oct 1
Externally published	Yes

Keywords

Bulk statistics
Gaussian beta ensembles
Global fluctuations
High temperature
Poisson statistics
Random Jacobi matrices

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s10955-018-2131-9

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title = "Gaussian Beta Ensembles at High Temperature: Eigenvalue Fluctuations and Bulk Statistics",

abstract = "We study the limiting behavior of Gaussian beta ensembles in the regime where βn= const as n→ ∞. 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 P{\'e}ch{\'e} (J Stat Phys 161(3):633–656, 2015) with the explicit form of the intensity measure.",

keywords = "Bulk statistics, Gaussian beta ensembles, Global fluctuations, High temperature, Poisson statistics, Random Jacobi matrices",

author = "Fumihiko Nakano and Trinh, {Khanh Duy}",

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T1 - Gaussian Beta Ensembles at High Temperature

T2 - Eigenvalue Fluctuations and Bulk Statistics

AU - Nakano, Fumihiko

AU - Trinh, Khanh Duy

N1 - Funding Information: This work is partially supported by JSPS KAKENHI Grant Numbers JP26400145 (F.N.) and JP16K17616 (K.D.T). Publisher Copyright: © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - We study the limiting behavior of Gaussian beta ensembles in the regime where βn= const as n→ ∞. 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.

AB - We study the limiting behavior of Gaussian beta ensembles in the regime where βn= const as n→ ∞. 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.

KW - Bulk statistics

KW - Gaussian beta ensembles

KW - Global fluctuations

KW - High temperature

KW - Poisson statistics

KW - Random Jacobi matrices

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Gaussian Beta Ensembles at High Temperature: Eigenvalue Fluctuations and Bulk Statistics

Abstract

Keywords

ASJC Scopus subject areas

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