Global spectrum fluctuations for Gaussian beta ensembles: a martingale approach

Research output: Contribution to journalArticlepeer-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 languageEnglish
JournalUnknown Journal
Publication statusPublished - 2017 Oct 11
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • General

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