Random walks on strict partitions

L. Petrov

Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XVII, Tome 373 (2009), pp. 226-272

Résumé

We construct a diffusion process in the infinite-dimensional simplex consisting of all nonincreasing infinite sequences of nonnegative numbers with sum less than or equal to one. The process is constructed as a limit of a certain sequence of Markov chains. The state space of the $n$th chain is the set of all strict partitions of $n$ (that is, partitions without equal parts). As $n\to\infty$, these random walks converge to a continuous-time strong Markov process in the infinite-dimensional simplex. The process has continuous sample paths. The main result about the limit process is the expression of its pre-generator as a formal second order differential operator in a polynomial algebra. Bibl. – 30 titles.

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