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

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.