A pr 2 00 9 ANISOTROPIC YOUNG DIAGRAMS AND INFINITE-DIMENSIONAL DIFFUSION PROCESSES WITH THE JACK PARAMETER

@inproceedings{Olshanski2009AP2,
  title={A pr 2 00 9 ANISOTROPIC YOUNG DIAGRAMS AND INFINITE-DIMENSIONAL DIFFUSION PROCESSES WITH THE JACK PARAMETER},
  author={Grigori Olshanski},
  year={2009}
}
We construct a family of Markov processes with continuous sample trajectories on an infinite-dimensional space, the Thoma simplex. The family depends on three continuous parameters, one of which, the Jack parameter, is similar to the beta parameter in random matrix theory. The processes arise in a scaling limit transition from certain finite Markov chains, the so called up-down chains on the Young graph with the Jack edge multiplicities. Each of the limit Markov processes is ergodic and its… CONTINUE READING