Math @ Duke

Publications [#243449] of Richard T. Durrett
Papers Published
 Durrett, R; Schonmann, RH, Large deviations for the contact process and two dimensional percolation,
Probability Theory and Related Fields, vol. 77 no. 4
(1988),
pp. 583603, Springer Nature, ISSN 01788051 [doi]
(last updated on 2019/04/20)
Abstract: The following results are proved: 1) For the upper invariant measure of the basic onedimensional 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 twodimensional 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 SpringerVerlag.


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