Persistence of sums of correlated increments and clustering in cellular automata

Hanbaek Lyu and David Sivakoff

Stochastic Processes and their Applications, 2019, vol. 129, issue 4, 1132-1152

Abstract: Let T be the first return time to (−∞,0] of sums of increments given by a functional of a stationary Markov chain. We determine the asymptotic behavior of the survival probability, P(T≥t)∼Ct−1∕2 for an explicit constant C. Our analysis is based on a connection between the survival probability and the running maximum of the time-reversed process, and relies on a functional central limit theorem for Markov chains. As applications, we recover known clustering results for the 3-color cyclic cellular automaton and the Greenberg–Hastings model, and we prove a new clustering result for the 3-color firefly cellular automaton.

Keywords: Survival probability; Running maximum; Markov chain; Correlated increments; Cellular automata; Annihilating particle systems (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2018.04.012

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