Multilevel Dyson Brownian motions via Jack polynomials

Vadim Gorin, Mykhaylo Shkolnikov

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


We introduce multilevel versions of Dyson Brownian motions of arbitrary parameter β>0, generalizing the interlacing reflected Brownian motions of Warren for β=2. Such processes unify β corners processes and Dyson Brownian motions in a single object. Our approach is based on the approximation by certain multilevel discrete Markov chains of independent interest, which are defined by means of Jack symmetric polynomials. In particular, this approach allows to show that the levels in a multilevel Dyson Brownian motion are intertwined (at least for β≥1) and to give the corresponding link explicitly.

Original languageEnglish (US)
Pages (from-to)413-463
Number of pages51
JournalProbability Theory and Related Fields
Issue number3-4
StatePublished - Nov 27 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • 05E05
  • 60B20
  • 60H10
  • 82C22


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