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

Author

Listed:
  • Fontes, L. R.
  • Isopi, M.
  • Sidoravicius, V.

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].

Suggested Citation

  • Fontes, L. R. & Isopi, M. & Sidoravicius, V., 1996. "Analyticity of the density and exponential decay of correlations in 2-d bootstrap percolation," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 169-178, March.
    • Handle: RePEc:eee:spapps:v:62:y:1996:i:1:p:169-178
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