CHARACTERISTIC EXPONENTS FOR 2-DIMENSIONAL BOOTSTRAP PERCOLATION

Bootstrap percolation is a model in which an element of Z2 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 deltap2alpha 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.