Fixation for distributed clustering processes
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Sheffield_Fixation for distributed.pdf
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Author(s)
Louidor, O.
Newman, C. M.
Rolla, L. T.
Sidoravicius, V.
Hilario, M. R.
Sheffield, Scott Roger
Date Issued
March 2010
Journal
Communications on Pure and Applied Mathematics
Publisher
Wiley Blackwell
Citation
Hilário, M. R., O. Louidor, C. M. Newman, L. T. Rolla, S. Sheffield, and V. Sidoravicius. “Fixation for distributed clustering processes.” Communications on Pure and Applied Mathematics (2010).
Version
Author's final manuscript
Abstract
We study a discrete-time resource flow in Z[superscript 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.
Description
Author's final manuscript January 19, 2010
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1002/cpa.20321
