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2018 A central limit theorem for the gossip process
A.D. Barbour, Adrian Röllin
Electron. J. Probab. 23: 1-37 (2018). DOI: 10.1214/18-EJP248

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.

Citation

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A.D. Barbour. Adrian Röllin. "A central limit theorem for the gossip process." Electron. J. Probab. 23 1 - 37, 2018. https://doi.org/10.1214/18-EJP248

Information

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

zbMATH: 07021679
MathSciNet: MR3896860
Digital Object Identifier: 10.1214/18-EJP248

Subjects:
Primary: 60J85, 60K35, 92H30

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Vol.23 • 2018
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