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

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...

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Bibliographic Details
Published in:Journal of functional analysis 2012-07, Vol.263 (1), p.248-303
Main Authors: Borodin, Alexei, Olshanski, Grigori
Format: Article
Language:English
Subjects:
Gelfand–Tsetlin schemes
Markov processes
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Summary: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.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2012.03.018