Infinite-dimensional Diffusions Related to the Two-parameter Poisson-Dirichlet Distributions
The talk describes population genetics perspective behind infinite-dimensional diffusions preserving the two-parameter Poisson–Dirichlet distributions and related models. It is based on [2].
Infinite-Dimensional Diffusion Processes Approximated by Finite Markov Chains on Partitions
The talk describes algebraic/combinatorial perspective behind infinite-dimensional diffusions preserving the two-parameter Poisson–Dirichlet distributions and related models. It is based on [2], see also [4], [8]
Random Walks on Strict Partitions
We consider a certain sequence of random walks. The state space of the n-th random walk is the set of all strict partitions of n (that is, partitions without equal parts). We prove that, as n goes to infinity, these random walks converge to a continuous-time Markov process.
A Two-parameter Family of Infinite-dimensional Diffusions in the Kingman Simplex
The aim of the paper is to introduce a two-parameter family of infinite-dimensional diffusion processes $X(\alpha,\theta)$ related to Pitman’s two-parameter Poisson-Dirichlet distributions $PD(\alpha,\theta)$.