Markov processes on the path space of the Gelfand-Tsetlin graph and on its boundary

Alexei Borodin, Grigori Olshanski

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)

Abstract

We construct a four-parameter family of Markov processes on infinite Gelfand-Tsetlin schemes that preserve the class of central (Gibbs) measures. Any process in the family induces a Feller Markov process on the infinite-dimensional boundary of the Gelfand-Tsetlin graph or, equivalently, the space of extreme characters of the infinite-dimensional unitary group U(∞). The process has a unique invariant distribution which arises as the decomposing measure in a natural problem of harmonic analysis on U(∞) posed in Olshanski (2003) [44]. As was shown in Borodin and Olshanski (2005) [11], this measure can also be described as a determinantal point process with a correlation kernel expressed through the Gauss hypergeometric function.

Original languageEnglish
Pages (from-to)248-303
Number of pages56
JournalJournal of Functional Analysis
Volume263
Issue number1
DOIs
Publication statusPublished - 1 Jul 2012
Externally publishedYes

Keywords

  • Gelfand-Tsetlin schemes
  • Markov processes

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