Electronic Journal of Probability

A central limit theorem for the gossip process

A.D. Barbour and Adrian Röllin

Full-text: Open access

Abstract

The Aldous gossip process represents the dissemination of information in geographical space as a process of locally deterministic spread, augmented by random long range transmissions. Starting from a single initially informed individual, the proportion of individuals informed follows an almost deterministic path, but for a random time shift, caused by the stochastic behaviour in the very early stages of development. In this paper, it is shown that, even with the extra information available after a substantial development time, this broad description remains accurate to first order. However, the precision of the prediction is now much greater, and the random time shift is shown to have an approximately normal distribution, with mean and variance that can be computed from the current state of the process.

Article information

Source
Electron. J. Probab., Volume 23 (2018), paper no. 123, 37 pp.

Dates
Received: 26 June 2017
Accepted: 19 November 2018
First available in Project Euclid: 18 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1545102141

Digital Object Identifier
doi:10.1214/18-EJP248

Mathematical Reviews number (MathSciNet)
MR3896860

Zentralblatt MATH identifier
07021679

Subjects
Primary: 92H30 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60J85: Applications of branching processes [See also 92Dxx]

Keywords
gossip process deterministic approximation branching processes central limit theorem

Rights
Creative Commons Attribution 4.0 International License.

Citation

Barbour, A.D.; Röllin, Adrian. A central limit theorem for the gossip process. Electron. J. Probab. 23 (2018), paper no. 123, 37 pp. doi:10.1214/18-EJP248. https://projecteuclid.org/euclid.ejp/1545102141


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References

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