Open Access
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


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.


Download Citation

Enrique D. Andjel. "Characteristic Exponents for Two-Dimensional Bootstrap Percolation." Ann. Probab. 21 (2) 926 - 935, April, 1993.


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

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

Primary: 60K35

Keywords: Bootstrap percolation , characteristic exponents , exponential rates

Rights: Copyright © 1993 Institute of Mathematical Statistics

Vol.21 • No. 2 • April, 1993
Back to Top