Nucleation and growth in two dimensions

Bollobás, Béla; Griffiths, Simon; Morris, Robert; Rolla, Leonardo; Smith, Paul
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 {\$}\backslashmathbb{\{}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.
Research areas:
Type of Publication:
Hits: 3409

We use cookies to improve our website and your experience when using it. Cookies used for the essential operation of this site have already been set. To find out more about the cookies we use and how to delete them, see our privacy policy.

  I accept cookies from this site.
EU Cookie Directive Module Information