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Fixation for distributed clustering processes

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Hilário, M. R., Louidor, O., Newman, C. M., Rolla, L. T., Sheffield, S. and Sidoravicius, V. (2010) Fixation for distributed clustering processes. Communications on Pure and Applied Mathematics, 63 (7). pp. 926-934. doi:10.1002/cpa.20321 ISSN 0010-3640.

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Official URL: http://dx.doi.org/10.1002/cpa.20321

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Abstract

We study a discrete‐time resource flow in \input amssym ${\Bbb 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.

Item Type: Journal Article
Divisions: Faculty of Science, Engineering and Medicine > Science > Statistics
Journal or Publication Title: Communications on Pure and Applied Mathematics
Publisher: John Wiley & Sons
ISSN: 0010-3640
Official Date: July 2010
Dates:
DateEvent
July 2010Published
15 March 2010Available
Volume: 63
Number: 7
Page Range: pp. 926-934
DOI: 10.1002/cpa.20321
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access

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