December 2013 Asymptotic behaviour of gossip processes and small-world networks
A. D. Barbour, G. Reinert
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Adv. in Appl. Probab. 45(4): 981-1010 (December 2013). DOI: 10.1239/aap/1386857854

Abstract

Both small-world models of random networks with occasional long-range connections and gossip processes with occasional long-range transmission of information have similar characteristic behaviour. The long-range elements appreciably reduce the effective distances, measured in space or in time, between pairs of typical points. In this paper we show that their common behaviour can be interpreted as a product of the locally branching nature of the models. In particular, it is shown that both typical distances between points and the proportion of space that can be reached within a given distance or time can be approximated by formulae involving the limit random variable of the branching process.

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A. D. Barbour. G. Reinert. "Asymptotic behaviour of gossip processes and small-world networks." Adv. in Appl. Probab. 45 (4) 981 - 1010, December 2013. https://doi.org/10.1239/aap/1386857854

Information

Published: December 2013
First available in Project Euclid: 12 December 2013

zbMATH: 1308.60107
MathSciNet: MR3161293
Digital Object Identifier: 10.1239/aap/1386857854

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

Keywords: branching process approximation , gossip process , Small-world graph

Rights: Copyright © 2013 Applied Probability Trust

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Vol.45 • No. 4 • December 2013
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