Global Spectrum Fluctuations for Gaussian Beta Ensembles: A Martingale Approach

Khanh Duy Trinh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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
Issue number3
Publication statusPublished - 2019 Sept 1
Externally publishedYes


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

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Global Spectrum Fluctuations for Gaussian Beta Ensembles: A Martingale Approach'. Together they form a unique fingerprint.

Cite this