Intertwinings of beta-Dyson Brownian motions of different dimensions

Kavita Ramanan, Mykhaylo Shkolnikov

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

We show that for all positive β the semigroups of β-Dyson Brownian motions of different dimensions are intertwined. The proof relates β-Dyson Brownian motions directly to Jack symmetric polynomials and omits an approximation of the former by discrete space Markov chains, thereby disposing of the technical assumption β ≥ 1 in (Probab. Theory Related Fields 163 (2015) 413–463). The corresponding results for β-Dyson Ornstein–Uhlenbeck processes are also presented.

Original languageEnglish (US)
Pages (from-to)1152-1163
Number of pages12
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume54
Issue number2
DOIs
StatePublished - May 2018

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Dixon–Anderson conditional probability density
  • Dyson Brownian motions
  • Dyson Ornstein–Uhlenbeck processes
  • Gaussian random matrix ensembles
  • Intertwinings
  • Jack symmetric polynomials

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