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Title: Nucleation and growth in two dimensions

We consider a dynamical process on a graphG, 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, 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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Award ID(s):
1855745
NSF-PAR ID:
10121819
Author(s) / Creator(s):
 ;  ;  ;  ;  
Publisher / Repository:
Wiley Blackwell (John Wiley & Sons)
Date Published:
Journal Name:
Random Structures & Algorithms
Volume:
56
Issue:
1
ISSN:
1042-9832
Page Range / eLocation ID:
p. 63-96
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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