Geodesic
Non-colliding Jacobi processes as limits of Markov chains on the Gelfand--Tsetlin graph
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamics systems, combinatorial methods. Part XVI, Tome 360 (2008), pp. 91-123

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We introduce a stochastic dynamics related to the measures that arise in the harmonic analysis on the infinite-dimensional unitary group. Our dynamics is obtained as a limit of a sequence of natural Markov chains on the Gelfand–Tsetlin graph. We compute the finite-dimensional distributions of the limit Markov process, as well as the generator and eigenfunctions of the semigroup related to this process. The limit process can be identified with the Doob $h$-transform of a family of independent diffusions. The space-time correlation functions of the limit process have a determinantal form. Bibl. – 21 titles. 
@article{ZNSL_2008_360_a3,
     author = {V. E. Gorin},
     title = {Non-colliding {Jacobi} processes as limits of {Markov} chains on the {Gelfand--Tsetlin} graph},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {91--123},
     publisher = {mathdoc},
     volume = {360},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_360_a3/}
}
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V. E. Gorin. Non-colliding Jacobi processes as limits of Markov chains on the Gelfand--Tsetlin graph. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamics systems, combinatorial methods. Part XVI, Tome 360 (2008), pp. 91-123. http://geodesic.mathdoc.fr/item/ZNSL_2008_360_a3/