| Full text | |
| Author(s): |
Hilario, M. R.
[1]
;
Louidor, O.
[2]
;
Newman, C. M.
[2]
;
Rolla, L. T.
[3]
;
Sheffield, S.
[4]
;
Sidoravicius, V.
[1, 5]
Total Authors: 6
|
| Affiliation: | [1] Inst Matematica Pura & Aplicada, BR-22460320 Rio De Janeiro - Brazil
[2] NYU, Courant Inst, New York, NY 10012 - USA
[3] Ecole Normale Super, Dept Math & Applicat, F-75005 Paris - France
[4] MIT, Dept Math, Cambridge, MA 02139 - USA
[5] Ctr Wiskunde & Informat, NL-1090 GB Amsterdam - Netherlands
Total Affiliations: 5
|
| Document type: | Journal article |
| Source: | COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS; v. 63, n. 7, p. 926-934, JUL 2010. |
| Web of Science Citations: | 1 |
| Abstract | |
We study a discrete-time resource flow in 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. (C) 2010 Wiley Periodicals, Inc. (AU) | |