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arXiv · 1508.06267

Nucleation and growth in two dimensions

Béla Bollobás·Simon Griffiths·Robert Morris·Leonardo Rolla·Paul Smith
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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 neighbours 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 $\mathbb{Z}^2$, 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.

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Béla Bollobás, Simon Griffiths, Robert Morris, Leonardo Rolla, Paul Smith. 2015-08-25. Nucleation and growth in two dimensions. https://arxiv.org/abs/1508.06267

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