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The topological support of the z-measures on the Thoma simplex
Grigori Olshanski · 2018-09-19 · via math.PR updates on arXiv.org

The Thoma simplex $Ω$ is an infinite-dimensional space, a kind of dual object to the infinite symmetric group. The z-measures are a family of probability measures on $Ω$ depending on three continuous parameters. One of them is the parameter of the Jack symmetric functions, and in the limit when it goes to $0$, the z-measures turn into the Poisson-Dirichlet distributions. The definition of the z-measures is somewhat implicit. We show that the topological support of any nondegenerate z-measure is the whole space $Ω$. The proof is based on results of arXiv:0902.3395 and arXiv:1806.07454.

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