Fixation for distributed clustering processes

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

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)926-934
Number of pages9
JournalCommunications on Pure and Applied Mathematics
Issue number7
StatePublished - Jul 2010

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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