Fixation for distributed clustering processes

M. R. Hilário; C. M. Newman; S. Sheffield; O. Louidor; L. T. Rolla; V. Sidoravicius

doi:10.1002/cpa.20321

Fixation for distributed clustering processes

M. R. Hilário, C. M. Newman, S. Sheffield, O. Louidor, L. T. Rolla, V. Sidoravicius

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 mass transport principle and extends to other graphs.

Original language	English (US)
Pages (from-to)	926-934
Number of pages	9
Journal	Communications on Pure and Applied Mathematics
Volume	63
Issue number	7
DOIs	https://doi.org/10.1002/cpa.20321
State	Published - Jul 2010

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1002/cpa.20321

Cite this

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AU - Louidor, O.

AU - Rolla, L. T.

AU - Sidoravicius, V.

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Fixation for distributed clustering processes

Abstract

ASJC Scopus subject areas

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