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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 extreme characters of the infinite-dimensional unitary group
U(infinity). The process has a unique invariant distribution which arises as
the decomposing measure in a natural problem of harmonic analysis on
U(infinity) posed in arXiv:math/0109193. As was shown in arXiv:math/0109194,
this measure can also be described as a determinantal point process with a
correlation kernel expressed through the Gauss hypergeometric function
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