International Journal of Stochastic Analysis

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International Journal of Stochastic Analysis / 2001 / Article

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Volume 14 |Article ID 476764 | 12 pages | https://doi.org/10.1155/S1048953301000193

The asymptotic behavior of elementary symmetric functions on a probability distribution

V. S. Kozyakin1 and A. V. Pokrovskii2,3

1Institute for Information Transmission Problems, 19 Bolshoi Karetny Lane, Russia

2National University of Ireland, Institute for Nonlinear Science, Department of Physics, University College, Ireland

3Institute of Information Transmission Problems, Russian Academy of Science, 19 Bolshoi Karetny Lane, Russia

Received01 Jul 1999
Revised01 Aug 2000

Abstract

The problem on asymptotic of the value π(m,n)=m!σm(p(1,n),p(2,n),…,p(n,n)) is considered, where σm(x1,x2,…,xn) is the mth elementary symmetric function of n variables. The result is interpreted in the context of nonequiprobable random mappings theory.

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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