Global spectrum fluctuations for Gaussian beta ensembles: a martingale approach

Khanh Duy Trinh

Global spectrum fluctuations for Gaussian beta ensembles: a martingale approach

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

Abstract

The paper describes the global limiting behavior of Gaussian beta ensembles where the parameter β is allowed to vary with the matrix size n. In particular, we show that as n → ∞ with nβ → ∞, the empirical distribution converges weakly to the semicircle distribution, almost surely. The Gaussian fluctuation around the limit is then derived by a martingale approach.

60B20 (Primary), 60F05 (Secondary)

Original language	English
Journal	Unknown Journal
Publication status	Published - 2017 Oct 11
Externally published	Yes

Keywords

Gaussian beta ensembles
Martingale difference central limit theorem
Semicircle law
Tridiagonal random matrices

ASJC Scopus subject areas

General

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title = "Global spectrum fluctuations for Gaussian beta ensembles: a martingale approach",

abstract = "The paper describes the global limiting behavior of Gaussian beta ensembles where the parameter β is allowed to vary with the matrix size n. In particular, we show that as n → ∞ with nβ → ∞, the empirical distribution converges weakly to the semicircle distribution, almost surely. The Gaussian fluctuation around the limit is then derived by a martingale approach.60B20 (Primary), 60F05 (Secondary)",

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KW - Martingale difference central limit theorem

KW - Semicircle law

KW - Tridiagonal random matrices

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