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arXiv · 0812.3146

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

Vadim Gorin
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Abstract

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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Vadim Gorin. 2008-12-16. Non-colliding Jacobi processes as limits of Markov chains on Gelfand-Tsetlin graph. https://arxiv.org/abs/0812.3146

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