Empires and percolation: stochastic merging of adjacent regions
نویسندگان
چکیده
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.
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