Work

Fixation for distributed clustering processes

Year: 2010

Type: article

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. © 2010 Wiley Periodicals, Inc.

Source: Communications on Pure and Applied Mathematics

DOI: 10.1002/cpa.20321

Authors: M. R. Hilário, O. Louidor, C. M. Newman, L. T. Rolla, S. Sheffield, V. Sidoravicius

Institutions: Instituto Nacional de Matemática Pura e Aplicada, Courant Institute of Mathematical Sciences, New York University, École Normale Supérieure - PSL, Département de mathématiques et applications, Massachusetts Institute of Technology, Centrum Wiskunde & Informatica

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2133923947

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Cites: 3

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