Functional Analysis and Its Applications

, Volume 52, Issue 4, pp 308–310 | Cite as

The Topological Support of the z-Measures on the Thoma Simplex

  • G. I. OlshanskiEmail author
Brief Communications


The Thoma simplex Ω is an infinite-dimensional space, a kind of dual object to the infinite symmetric group. The z-measures are probability measures on Ω depending on three continuous parameters. One of them is the parameter of the Jack symmetric functions, and in the limit as 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.

Key words

z-measure Poisson–Dirichlet distribution topological support symmetric function 


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Institute for Information Transmission ProblemsMoscowRussia
  2. 2.Skolkovo Institute of Science and TechnologyMoscowRussia
  3. 3.Department of MathematicsNational Research University Higher School of EconomicsMoscowRussia

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