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Escape of resources in a distributed clustering process

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Escape of resources in a distributed clustering process
2.	Creator	Author's name, affiliation, country	Jacob van den Berg; CWI and VU University Amsterdam
2.	Creator	Author's name, affiliation, country	Marcelo Richard Hilário; IMPA
2.	Creator	Author's name, affiliation, country	Alexander E. Holroyd; Microsoft Research and University of British Columbia
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Clustering process, random spanning tree
3.	Subject	Subject classification	60K35; 68M14
4.	Description	Abstract	In a distributed clustering algorithm introduced by Coffman, Courtois, Gilbert and Piret [1], each vertex of $\mathbb{Z}^d$ receives an initial amount of a resource, and, at each iteration, transfers all of its resource to the neighboring vertex which currently holds the maximum amount of resource. In [4] it was shown that, if the distribution of the initial quantities of resource is invariant under lattice translations, then the flow of resource at each vertex eventually stops almost surely, thus solving a problem posed in [2]. In this article we prove the existence of translation-invariant initial distributions for which resources nevertheless escape to infinity, in the sense that the the final amount of resource at a given vertex is strictly smaller in expectation than the initial amount. This answers a question posed in [4].
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	CNPq; NSERC
7.	Date	(YYYY-MM-DD)	2010-09-30
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1567
10.	Identifier	Digital Object Identifier	10.1214/ECP.v15-1567
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 15
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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