Cesaro mean distribution of group automata starting from measures with summable decay
Probability
2011-11-10 v1 Dynamical Systems
Abstract
Consider a finite Abelian group (G,+), with |G|=p^r, p a prime number, and F: G^N -> G^N the cellular automaton given by {F(x)}_n= A x_n + B x_{n+1} for any n in N, where A and B are integers relatively primes to p. We prove that if P is a translation invariant probability measure on G^Z determining a chain with complete connections and summable decay of correlations, then for any w= (w_i:i<0) the Cesaro mean distribution of the time iterates of the automaton with initial distribution P_w --the law P conditioned to w on the left of the origin-- converges to the uniform product measure on G^N. The proof uses a regeneration representation of P.
Keywords
Cite
@article{arxiv.math/9912135,
title = {Cesaro mean distribution of group automata starting from measures with summable decay},
author = {Pablo A. Ferrari and Alejandro Maass and Servet Martinez and Peter Ney},
journal= {arXiv preprint arXiv:math/9912135},
year = {2011}
}