A Smooth Transition from Wishart to GOE

Miklós Z. Rácz, Jacob Richey

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

It is well known that an n× n Wishart matrix with d degrees of freedom is close to the appropriately centered and scaled Gaussian orthogonal ensemble (GOE) if d is large enough. Recent work of Bubeck, Ding, Eldan, and Racz, and independently Jiang and Li, shows that the transition happens when d= Θ (n 3 ). Here we consider this critical window and explicitly compute the total variation distance between the Wishart and GOE matrices when d/ n 3 → c∈ (0 , ∞). This shows, in particular, that the phase transition from Wishart to GOE is smooth.

Original languageEnglish (US)
Pages (from-to)898-906
Number of pages9
JournalJournal of Theoretical Probability
Volume32
Issue number2
DOIs
StatePublished - Jun 1 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

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

Keywords

  • Gaussian Orthogonal Ensemble (GOE)
  • Phase transition
  • Random matrix theory
  • Total variation
  • Wishart distribution

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