Electronic Journal of Probability

A central limit theorem for the gossip process

A.D. Barbour and Adrian Röllin

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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

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

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

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Zentralblatt MATH identifier

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

gossip process deterministic approximation branching processes central limit theorem

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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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