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- W51962510 abstract "We study a two-parametric family of probability measures on an infinite-dimensional simplex (the Thoma simplex). These measures originate in harmonic analysis on the infinite symmetric group (17). Our approach is to interpret them as probability distributions on a space of point configurations, i.e., as certain point stochastic processes, and to find the correlation functions of these processes. In this paper we relate the correlation functions to the solutions of certain multidimensional moment problems. Then we calculate the first correlation function which leads to a conclusion about the support of the initial measures. In the appendix, we discuss a parallel but more elementary theory related to the well-known Poisson—Dirichlet distribution. The paper is part of a joint project with Alexei Borodin and can serve as an introduction to the subject. The goal of our work is to understand new phenomena in noncom-mutative harmonic analysis which arise when the irreducible representations depend on countably many continuous parameters." @default.
- W51962510 created "2016-06-24" @default.
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- W51962510 date "2003-01-01" @default.
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- W51962510 title "Point Processes Related to the Infinite Symmetric Group" @default.
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- W51962510 doi "https://doi.org/10.1007/978-1-4612-0029-1_15" @default.
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