Geodesic
The Topological Support of the z-Measures on the Thoma Simplex
Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 4, pp. 86-88

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The Thoma simplex $\Omega$ is an infinite-dimensional space, a kind of dual object to the infinite symmetric group. The z-measures are probability measures on $\Omega$ 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 $\Omega$.
Keywords: z-measure, topological support, symmetric function.
Mots-clés : Poisson-Dirichlet distribution 
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     author = {G. I. Olshanskii},
     title = {The {Topological} {Support} of the {z-Measures} on the {Thoma} {Simplex}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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G. I. Olshanskii. The Topological Support of the z-Measures on the Thoma Simplex. Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 4, pp. 86-88. http://geodesic.mathdoc.fr/item/FAA_2018_52_4_a5/