Transition Density of an Infinite-dimensional diffusion with the Jack Parameter
arXiv:2102.12681
Abstract
From the Poisson-Dirichlet diffusions to the -measure diffusions, they all have explicit transition densities. In this paper, we will show that the transition densities of the -measure diffusions can also be expressed as a mixture of a sequence of probability measures on the Thoma simplex. The coefficients are still the transition probabilities of the Kingman coalescent stopped at state . This fact will be uncovered by a dual process method in a special case where the -measure diffusions is established through up-down chain in the Young graph.
16 pages