Analyticity of the density and exponential decay of correlations in 2-d bootstrap percolation

L. R. Fontes, M. Isopi and V. Sidoravicius

Stochastic Processes and their Applications, 1996, vol. 62, issue 1, 169-178

Abstract: We consider some deterministic cellular automata on the state space {0, 1}d, starting from the product of Bernoulli measures and evolving in discrete time according to the bootstrap percolation rules, in which a 0 changes to a 1 when it has at least l neighbours which are 1. We prove that in case l = 2d - 1 the limiting measure has an exponential decay of correlations and the density function is analytic in [0, 1].

Keywords: Bootstrap; percolation; Analyticity; Exponential; decay (search for similar items in EconPapers)
Date: 1996
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