Abstract
Bootstrap percolation is a model in which an element of $\mathbf{Z}^2$ becomes occupied in one time unit if two appropriately chosen neighbors are occupied. Schonmann [4] proved that starting from a Bernoulli product measure of positive density, the distribution of the time needed to occupy the origin decays exponentially. We show that for $\alpha > 1$, the exponent can be taken as $\delta p^{2\alpha}$ for some $\delta > 0$, thus showing that the associated characteristic exponent is at most two. Another characteristic exponent associated to this model is shown to be equal to one.
Citation
Enrique D. Andjel. "Characteristic Exponents for Two-Dimensional Bootstrap Percolation." Ann. Probab. 21 (2) 926 - 935, April, 1993. https://doi.org/10.1214/aop/1176989275
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