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 Z2, 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.
Random Structures and Algorithms
Bollobás, B., Griffiths, S., Morris, R., T Rolla, L., & Smith, P. (2020). Nucleation and growth in two dimensions. Random Structures and Algorithms, 56 (1), 63-96. https://doi.org/10.1002/rsa.20888