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Cesaro mean distribution of group automata starting from measures with summable decay | | Pablo A. Ferrari
; Alejandro Maass
; Servet Martinez
; Peter Ney
; | | Date: |
16 Dec 1999 | | Journal: | Ergodic Theory and Dynamical Systems (2000) | | Subject: | Probability; Dynamical Systems MSC-class: 60K35, 82C, 60K05, 60J05, 58F08 | math.PR math.DS | | 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. | | Source: | arXiv, math.PR/9912135 | | Services: | Forum | Review | PDF | Favorites | |
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