Invariant Measures and Decay of Correlations for a Class of Ergodic Probabilistic Cellular Automata

Autor(es)

Coletti, Cristian F. ^[1] ; Tisseur, Pierre ^[1]

Afiliação do(s) autor(es)

^[1] Univ Fed ABC, Ctr Matemat Cognicao & Computacao, Santo Andre, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Statistical Physics; v. 140, n. 1, p. 103-121, JUL 2010.
• Citações Web of Science: 3

Resumo

We give new sufficient ergodicity conditions for two-state probabilistic cellular automata (PCA) of any dimension and any radius. The proof of this result is based on an extended version of the duality concept. Under these assumptions, in the one dimensional case, we study some properties of the unique invariant measure and show that it is shift-mixing. Also, the decay of correlation is studied in detail. In this sense, the extended concept of duality gives exponential decay of correlation and allows to compute explicitly all the constants involved. (AU)

• Processo FAPESP: 06/54511-2 - Convergência de curvas aleatórias
• Beneficiário: Cristian Favio Coletti
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado