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

Understand

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.