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Critical length for semi-oriented bootstrap percolation

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  • Mountford, T. S.

Abstract

We consider the behaviour of semi-oriented bootstrap percolation restricted to a finite square or torus. We prove that as the probability of initial occupancy p tends to zero, the side length required for a two-dimensional torus to have non-negligible chance of filling itself up is between for universal constants c and C. We show similar results for the side length required for a square to show significant clustering behaviour.

Suggested Citation

  • Mountford, T. S., 1995. "Critical length for semi-oriented bootstrap percolation," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 185-205, April.
    • Handle: RePEc:eee:spapps:v:56:y:1995:i:2:p:185-205
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    References listed on IDEAS

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    1. Adler, Joan, 1991. "Bootstrap percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 171(3), pages 453-470.
    2. Duarte, J.A.M.S., 1989. "Simulation of a cellular automat with an oriented bootstrap rule," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 157(3), pages 1075-1079.
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    Cited by:

    1. Cerf, R. & Manzo, F., 2002. "The threshold regime of finite volume bootstrap percolation," Stochastic Processes and their Applications, Elsevier, vol. 101(1), pages 69-82, September.

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