Point processes and the infinite symmetric group
نویسندگان
چکیده
منابع مشابه
Point Processes and the Infinite Symmetric Group Part Iii: Fermion Point Processes
In Part I (G. Olshanski) and Part II (A. Borodin) we developed an approach to certain probability distributions on the Thoma simplex. The latter has infinite dimension and is a kind of dual object for the infinite symmetric group. Our approach is based on studying the correlation functions of certain related point stochastic processes. In the present paper we consider the so–called tail point p...
متن کاملPoint Processes and the Infinite Symmetric Group. Part I: the General Formalism and the Density Function
We study a 2-parametric family of probability measures on an infinite– dimensional simplex (the Thoma simplex). These measures originate in harmonic analysis on the infinite symmetric group (S. Kerov, G. Olshanski and A. Vershik, Comptes Rendus Acad. Sci. Paris I 316 (1993), 773-778). Our approach is to interprete them as probability distributions on a space of point configurations, i.e., as ce...
متن کاملPoint Processes and the Infinite Symmetric Group. Part V: Analysis of the Matrix Whittaker Kernel
The matrix Whittaker kernel has been introduced by A. Borodin in Part IV of the present series of papers. This kernel describes a point process — a probability measure on a space of countable point configurations. The kernel is expressed in terms of the Whittaker confluent hypergeometric functions. It depends on two parameters and determines a J-symmetric operator K in L(R+)⊕ L(R+). It turns ou...
متن کاملPoint Processes and the Infinite Symmetric Group Part Ii: Higher Correlation Functions
We continue the study of the correlation functions for the point stochastic processes introduced in Part I (G. Olshanski). We find an integral representation of all the correlation functions and their explicit expression in terms of multivariate hypergeometric functions. Then we define a modification (“lifting”) of the processes which results in a substantial simplification of the structure of ...
متن کاملPoint Processes and the Infinite Symmetric Group Part Iv: Matrix Whittaker Kernel
We study a 2–parametric family of probability measures on the space of countable point configurations on the punctured real line (the points of the random configuration are concentrated near zero). These measures (or, equivalently, point processes) have been introduced in Part II (A. Borodin, math/9804087) in connection with the problem of harmonic analysis on the infinite symmetric group. The ...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 1998
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.1998.v5.n6.a9