Fixation for Distributed Clustering Processes
Probability
2017-08-02 v3
Abstract
We study a discrete-time resource flow in , 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.
Keywords
Cite
@article{arxiv.0906.3154,
title = {Fixation for Distributed Clustering Processes},
author = {Marcelo R. Hilario and Oren Louidor and Charles M. Newman and Leonardo T. Rolla and Scott Sheffield and Vladas Sidoravicius},
journal= {arXiv preprint arXiv:0906.3154},
year = {2017}
}