Email this article The Topological Support of the z-Measures on the Thoma Simplex
- Authors: Olshanski G.I.1,2,3
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Affiliations:
- Institute for Information Transmission Problems
- Skolkovo Institute of Science and Technology
- Department of Mathematics, National Research University Higher School of Economics
- Issue: Vol 52, No 4 (2018)
- Pages: 308-310
- Section: Brief Communications
- URL: https://journals.rcsi.science/0016-2663/article/view/234551
- DOI: https://doi.org/10.1007/s10688-018-0240-5
- ID: 234551
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Abstract
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.
About the authors
G. I. Olshanski
Institute for Information Transmission Problems; Skolkovo Institute of Science and Technology; Department of Mathematics, National Research University Higher School of Economics
Author for correspondence.
Email: olsh2007@gmail.com
Russian Federation, Moscow; Moscow; Moscow
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