Markov Processes on the Path Space of the Gelfand-tsetlin Graph and on Its Boundary
نویسندگان
چکیده
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 [Ols03]. As was shown in [BO05a], 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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