Global Spectrum Fluctuations for Gaussian Beta Ensembles: A Martingale Approach

Khanh Duy Trinh

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)1420-1437
Number of pages18
JournalJournal of Theoretical Probability
Volume32
Issue number3
DOIs
Publication statusPublished - Sep 1 2019

Fingerprint

Martingale
Ensemble
Fluctuations
Semicircle
Empirical Distribution
Limiting Behavior
Vary
Converge
Empirical distribution
Martingale approach

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

Cite this

Global Spectrum Fluctuations for Gaussian Beta Ensembles : A Martingale Approach. / Trinh, Khanh Duy.

In: Journal of Theoretical Probability, Vol. 32, No. 3, 01.09.2019, p. 1420-1437.

Research output: Contribution to journalArticle

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