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Asymptotic behaviour of gossip processes and small-world networks


Barbour, A D; Reinert, Gesine (2013). Asymptotic behaviour of gossip processes and small-world networks. Advances in Applied Probability, 45(4):981-1010.

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.

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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2013
Deposited On:28 Dec 2017 14:47
Last Modified:18 Apr 2018 11:49
Publisher:Applied Probability Trust
ISSN:0001-8678
Funders:Schweizerischer Nationalfonds
OA Status:Green
Publisher DOI:https://doi.org/10.1017/S000186780000673X

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