Non-colliding Jacobi processes as limits of Markov chains on Gelfand-Tsetlin graph

Details Non-colliding Jacobi processes as limits of Markov chains on Gelfand-Tsetlin graph Non-colliding Jacobi processes as limits of Markov chains on Gelfand-Tsetlin graph

2008-12-16

arxiv.org/abs/0812.3146v1

Journal of Mathematical Sciences, 158 (2009), no. 6, 819-837 (translated from Zapiski Nauchnykh Seminarov POMI, 360 (2008), pp

Mathematics

Probability

28 pages

Scientific paper

We introduce a stochastic dynamics related to the measures that arise in harmonic analysis on the infinite-dimensional unitary group. Our dynamics is obtained as a limit of a sequence of natural Markov chains on Gelfand-Tsetlin graph. We compute finite-dimensional distributions of the limit Markov process, the generator and eigenfunctions of the semigroup related to this process. The limit process can be identified with Doob h-transform of a family of independent diffusions. Space-time correlation functions of the limit process have a determinantal form.

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