Nucleation and growth in two dimensions

We consider a dynamical process on a graph G, in which vertices are infected (randomly) at a rate which depends on the number of their neighbors that are already infected. This model includes bootstrap percolation and first-passage percolation as its extreme points. We give a precise description of the evolution of this process on the graph Z^2, significantly sharpening results of Dehghanpour and Schonmann. In particular, we determine the typical infection time up to a constant factor for almost all natural values of the parameters, and in a large range we obtain a stronger, sharp threshold.Fil: Bollobás, Béla. University of Cambridge; Estados Unidos. University of Memphis; Estados UnidosFil: Griffiths, Simon. Conselho Nacional de Desenvolvimiento Cientf y Tec. Associacao Instituto Nacional de Matemática Pura E Aplicada; BrasilFil: Morris, Robert. Conselho Nacional de Desenvolvimiento Cientf y Tec. Associacao Instituto Nacional de Matemática Pura E Aplicada; BrasilFil: Trivellato Rolla, Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Smith, Paul. Conselho Nacional de Desenvolvimiento Cientf y Tec. Associacao Instituto Nacional de Matemática Pura E Aplicada; Brasi