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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
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: |
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| 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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