Nucleation and growth in two dimensions

Authors

Béla Bollobás, Faculty of MathematicsFollow
Simon Griffiths, Pontifícia Universidade Católica do Rio de Janeiro
Robert Morris, Instituto Nacional de Matematica Pura E Aplicada, Rio de Janeiro
Leonardo T Rolla, Universidad de Buenos Aires
Paul Smith, Instituto Nacional de Matematica Pura E Aplicada, Rio de Janeiro

Abstract

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.

Publication Title

Random Structures and Algorithms

Recommended Citation

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