Fixation for distributed clustering processes
Author(s)
Louidor, O.; Newman, C. M.; Rolla, L. T.; Sidoravicius, V.; Hilario, M. R.; Sheffield, Scott Roger; ... Show more Show less
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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
Date issued
2010-03Department
Massachusetts Institute of Technology. Department of MathematicsJournal
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
ISSN
00103640
10970312