The Skitovich-Darmois theorem for finite Abelian groups
Probability
2011-06-22 v1
Abstract
Let X be a finite Abelian group, xi_i, i=1,2,...,n,n>1, be independent random variables with values in X and distributions mu_i. Let alpha_{ij},i,j=1,2,...,n, be automorphisms of X. We prove that the independence of n linear forms L_j=alpha_{1j}xi_1+alpha_{2j}xi_2+...+alpha_{nj}xi_n implies that all mu_i are shifts of the Haar distributions on some subgroups of the group X. This theorem is an analogue of the Skitovich-Darmois theorem for finite Abelian groups.
Keywords
Cite
@article{arxiv.1106.4134,
title = {The Skitovich-Darmois theorem for finite Abelian groups},
author = {Ivan Mazur},
journal= {arXiv preprint arXiv:1106.4134},
year = {2011}
}