Random Walks on Strict Partitions

[2009/04/10]

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.

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A dynamics of the four most common alleles. The hitting of finite-dimensional subspaces is evident

A Two-parameter Family of Infinite-dimensional Diffusions in the Kingman Simplex

[2007/08/16]

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 $PD(\alpha,\theta)$.

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