Fixation for Distributed Clustering Processes

Details Fixation for Distributed Clustering Processes Fixation for Distributed Clustering Processes

2009-06-17

arxiv.org/abs/0906.3154v2

Communications on Pure and Applied Mathematics, v. 63, p. 926-934, 2010

Mathematics

Probability

9 pages, 1 figure. Minor corrections

Scientific paper

We study a discrete-time resource flow in $Z^d$, where wealthier vertices attract the resources of their less rich neighbors. For any translation-invariant probability distribution of initial resource quantities, we prove that the flow at each vertex terminates after finitely many steps. This answers (a generalized version of) a question posed by van den Berg and Meester in 1991. The proof uses the mass-transport principle and extends to other graphs.

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