Markov processes on the path space of the Gelfand-Tsetlin graph and on its boundary
Probability
2013-03-04 v1 Mathematical Physics
math.MP
Representation Theory
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(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.
Keywords
Cite
@article{arxiv.1009.2029,
title = {Markov processes on the path space of the Gelfand-Tsetlin graph and on its boundary},
author = {Alexei Borodin and Grigori Olshanski},
journal= {arXiv preprint arXiv:1009.2029},
year = {2013}
}