Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Empires and Percolation: Stochastic Merging of Adjacent Regions   We introduce a stochastic model in which adjacent planar regions $A, B$ merge
stochastically at some rate $\lambda(A,B)$, 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 $\lambda$
for this {\em 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 $\lambda(A,B) \equiv 1$. For this case, a non-rigorous analytic
argument and simulations suggest hegemony.

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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: eess
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
1
The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga