Fixation for distributed clustering processes

• Main Authors: Louidor, O. (Author), Newman, C. M. (Author), Rolla, L. T. (Author), Sidoravicius, V. (Author), Hilario, M. R. (Author), Sheffield, Scott Roger (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
• Format: Article
• Language: English
• Published: Wiley Blackwell, 2013-09-16T12:24:41Z.
• Subjects: Article
• Online Access: Get fulltext

Author's final manuscript January 19, 2010
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.
National Science Foundation (U.S.) (Grant DMS-06-45585)
National Science Foundation (U.S.) (Grant OISE-07-30136)