Fixation for Distributed Clustering Processes
نویسندگان
چکیده
We study a discrete-time resource flow in Zd, 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 masstransport principle and extends to other graphs. AMS Subject Classifications: 60K35, 90B15, 68M14.
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