Stationary random partitions of positive integers.
Prob. Theory Appl., 44, No. 1 (1999), 60-74.

Abstract. We describe stationary random partitions of positive integers (in equivalent setting - of stationary coherent sequences of random permutations) with respect to a natural action of the infinite symmetric group. The result yields a new characterization of the Poisson-Dirichlet distribution PD(1) as the unique invariant distribution for a family of Markovian operators on the infinite-dimensional simplex, as well as a new characterization of the Haar measure on the projective limit of finite symmetric groups.

Back to the list of papers