Random walks on strict partitions

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.