Publications [#243449] of Richard T. Durrett

Papers Published

1. Durrett, R; Schonmann, RH, Large deviations for the contact process and two dimensional percolation, Probability Theory and Related Fields, vol. 77 no. 4 (December, 1988), pp. 583-603, Springer Nature, ISSN 0178-8051 [doi]
   (last updated on 2024/04/16)

   Abstract:
   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.