BibTeX
@MISC{Aldous09adjacentregions,
author = {D J Aldous and J R Ong and W Zhou},
title = {adjacent regions},
year = {2009}
}
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Abstract
We introduce a stochastic model in which adjacent planar regions A, B merge stochastically at some rate λ(A, B) and observe analogies with the well-studied topics of mean-field coagulation and of bond percolation. Do infinite regions appear in finite time? We give a simple condition on λ for this hegemony property to hold, and another simple condition for it to not hold, but there is a large gap between these conditions, which includes the case λ(A, B) ≡ 1. For this case, a non-rigorous analytic argument and simulations suggest hegemony. PACS number: 64.60.ah (Some figures in this article are in colour only in the electronic version) 1.
