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Nucleation and growth in two dimensions
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Bollobás, Béla, Griffiths, Simon, Morris, Robert, Rolla, Leonardo T. and Smith, Paul (2020) Nucleation and growth in two dimensions. Random Structures & Algorithms, 56 (1). pp. 63-96. doi:10.1002/rsa.20888 ISSN 1042-9832.
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Official URL: http://dx.doi.org/10.1002/rsa.20888
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 urn:x-wiley:rsa:media:rsa20888:rsa20888-math-0001, 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.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
| Journal or Publication Title: | Random Structures & Algorithms | ||||||
| Publisher: | John Wiley & Sons, Inc. | ||||||
| ISSN: | 1042-9832 | ||||||
| Official Date: | January 2020 | ||||||
| Dates: |
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| Volume: | 56 | ||||||
| Number: | 1 | ||||||
| Page Range: | pp. 63-96 | ||||||
| DOI: | 10.1002/rsa.20888 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access |
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