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April, 1993 Characteristic Exponents for Two-Dimensional Bootstrap Percolation
Enrique D. Andjel
Ann. Probab. 21(2): 926-935 (April, 1993). DOI: 10.1214/aop/1176989275

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.

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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

Information

Published: April, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0787.60120
MathSciNet: MR1217573
Digital Object Identifier: 10.1214/aop/1176989275

Subjects:
Primary: 60K35

Keywords: Bootstrap percolation , characteristic exponents , exponential rates

Rights: Copyright © 1993 Institute of Mathematical Statistics

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Vol.21 • No. 2 • April, 1993
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