Electronic Communications in Probability

Escape of resources in a distributed clustering process

Jacob van den Berg, Marcelo Hilário, and Alexander Holroyd

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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].

Article information

Source
Electron. Commun. Probab., Volume 15 (2010), paper no. 40, 442-448.

Dates
Accepted: 30 September 2010
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465243983

Digital Object Identifier
doi:10.1214/ECP.v15-1567

Mathematical Reviews number (MathSciNet)
MR2726090

Zentralblatt MATH identifier
1226.60132

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 68M14: Distributed systems

Keywords
Clustering process random spanning tree

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

van den Berg, Jacob; Hilário, Marcelo; Holroyd, Alexander. Escape of resources in a distributed clustering process. Electron. Commun. Probab. 15 (2010), paper no. 40, 442--448. doi:10.1214/ECP.v15-1567. https://projecteuclid.org/euclid.ecp/1465243983


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References

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