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

Fumihiko Nakano, Khanh Duy Trinh

Research output: Contribution to journalArticle

2 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 languageEnglish
Pages (from-to)295-321
Number of pages27
JournalJournal of Statistical Physics
Volume173
Issue number2
DOIs
Publication statusPublished - 2018 Oct 1
Externally publishedYes

Fingerprint

Ensemble
eigenvalues
statistics
Fluctuations
Statistics
Eigenvalue
Limiting Behavior
Siméon Denis Poisson
Alternatives
Form

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

Cite this

Gaussian Beta Ensembles at High Temperature : Eigenvalue Fluctuations and Bulk Statistics. / Nakano, Fumihiko; Trinh, Khanh Duy.

In: Journal of Statistical Physics, Vol. 173, No. 2, 01.10.2018, p. 295-321.

Research output: Contribution to journalArticle

Nakano, Fumihiko ; Trinh, Khanh Duy. / Gaussian Beta Ensembles at High Temperature : Eigenvalue Fluctuations and Bulk Statistics. In: Journal of Statistical Physics. 2018 ; Vol. 173, No. 2. pp. 295-321.
@article{50ab1c9330c04afaa16579ec03c02da3,
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}",
year = "2018",
month = "10",
day = "1",
doi = "10.1007/s10955-018-2131-9",
language = "English",
volume = "173",
pages = "295--321",
journal = "Journal of Statistical Physics",
issn = "0022-4715",
publisher = "Springer New York",
number = "2",

}

TY - JOUR

T1 - Gaussian Beta Ensembles at High Temperature

T2 - Eigenvalue Fluctuations and Bulk Statistics

AU - Nakano, Fumihiko

AU - Trinh, Khanh Duy

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

UR - http://www.scopus.com/inward/record.url?scp=85051680090&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85051680090&partnerID=8YFLogxK

U2 - 10.1007/s10955-018-2131-9

DO - 10.1007/s10955-018-2131-9

M3 - Article

AN - SCOPUS:85051680090

VL - 173

SP - 295

EP - 321

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 2

ER -