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arXiv · 0906.3154

Fixation for Distributed Clustering Processes

Marcelo R. Hilario·Oren Louidor·Charles M. Newman·Leonardo T. Rolla·Scott Sheffield·Vladas Sidoravicius
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Abstract

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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Marcelo R. Hilario, Oren Louidor, Charles M. Newman, Leonardo T. Rolla, Scott Sheffield, Vladas Sidoravicius. 2017-08-01. Fixation for Distributed Clustering Processes. https://doi.org/10.1002/cpa.20321

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