Journal of Applied Mathematics and Stochastic Analysis
Volume 14 (2001), Issue 3, Pages 237-248
doi:10.1155/S1048953301000193
The asymptotic behavior of elementary symmetric functions on a probability distribution
1Institute for Information Transmission Problems, 19 Bolshoi Karetny Lane, Moscow 101447, Russia
2National University of Ireland, Institute for Nonlinear Science, Department of Physics, University College, Cork, Ireland
3Institute of Information Transmission Problems, Russian Academy of Science, 19 Bolshoi Karetny Lane, Moscow 101447, Russia
Received 1 July 1999; Revised 1 August 2000
Copyright © 2001 V. S. Kozyakin and A. V. Pokrovskii. 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.
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.