Fixation for distributed clustering processes

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

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)926-934
Number of pages9
JournalCommunications on Pure and Applied Mathematics
Volume63
Issue number7
DOIs
StatePublished - Jul 2010

Fingerprint

Fixation
Probability distributions
Mass transfer
Clustering
Resources
Invariant Distribution
Mass Transport
Terminate
Discrete-time
Probability Distribution
Graph in graph theory
Vertex of a graph

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Hilário, M. R., Newman, C., Sheffield, S., Louidor, O., Rolla, L. T., & Sidoravicius, V. (2010). Fixation for distributed clustering processes. Communications on Pure and Applied Mathematics, 63(7), 926-934. https://doi.org/10.1002/cpa.20321

Fixation for distributed clustering processes. / Hilário, M. R.; Newman, Charles; Sheffield, S.; Louidor, O.; Rolla, L. T.; Sidoravicius, V.

In: Communications on Pure and Applied Mathematics, Vol. 63, No. 7, 07.2010, p. 926-934.

Research output: Contribution to journalArticle

Hilário, MR, Newman, C, Sheffield, S, Louidor, O, Rolla, LT & Sidoravicius, V 2010, 'Fixation for distributed clustering processes', Communications on Pure and Applied Mathematics, vol. 63, no. 7, pp. 926-934. https://doi.org/10.1002/cpa.20321
Hilário MR, Newman C, Sheffield S, Louidor O, Rolla LT, Sidoravicius V. Fixation for distributed clustering processes. Communications on Pure and Applied Mathematics. 2010 Jul;63(7):926-934. https://doi.org/10.1002/cpa.20321
Hilário, M. R. ; Newman, Charles ; Sheffield, S. ; Louidor, O. ; Rolla, L. T. ; Sidoravicius, V. / Fixation for distributed clustering processes. In: Communications on Pure and Applied Mathematics. 2010 ; Vol. 63, No. 7. pp. 926-934.
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