Large deviations for the contact process and two dimensional percolation

The following results are proved: 1) For the upper invariant measure of the basic one-dimensional supercritical contact process the density of 1's has the usual large deviation behavior: the probability of a large deviation decays exponentially with the number of sites considered. 2) For supercritical two-dimensional nearest neighbor site (or bond) percolation the density YΛ of sites inside a square Λ which belong to the infinite cluster has the following large deviation properties. The probability that YΛ deviates from its expected value by a positive amount decays exponentially with the area of Λ, while the probability that it deviates from its expected value by a negative amount decays exponentially with the perimeter of Λ. These two problems are treated together in this paper because similar techniques (renormalization) are used for both. © 1988 Springer-Verlag.

Duke Scholars

Author Richard Timothy Durrett Mathematics