Stochastic Growth Models

Abstract

This paper is based on a talk given by the first author at the I.M.A. in February, 1986 but incorporates improvements discovered during six later repiti-tions. The second authour should not be held responsible for the style of presentation of the results but should be given credit for discovering the results independently in the Fall of 1985. The discussion below is equal to the talk with most of the details of the proofs filled in, but we have tried to preserve the informal style of the talk and concentrate on the “main ideas” rather than giving complete details of the proofs. If we forget about definitions then the results can be summed up in a few words “Everything Durrett and Griffeath (1983) proved for one-dimensional nearest neighbor additive groth models is true for the corresponding class of finite range models, i.e., those which can be constructed from a percolation structure.”

This author was partially supported by an NSF grant and an AMS “mid-career” fellowship.

This author was partially supported by CNPq (Brazil) and NSF during the academic year 1985–86 which he spent at the Rutgers Math department. He will visit the Cornell Mathematical Sciences Institute for 1986–87.