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Rumor Processes on N

Part of:Stochastic processesSpecial processes

Published online by Cambridge University Press:  14 July 2016

Valdivino V. Junior,
Fábio P. Machado and
Mauricio Zuluaga
Valdivino V. Junior*
Affiliation:
Universidade Federal de Goias
Fábio P. Machado*
Affiliation:
Universidade de São Paulo
Mauricio Zuluaga*
Affiliation:
Universidade de São Paulo
*
∗ Postal address: Institute of Mathematics and Statistics, Universidade Federal de Goias, Campus Samambaia, CEP 74001-970, Goiânia, GO, Brazil. Email address: vvjunior@mat.ufg.br
∗∗ Postal address: Institute of Mathematics and Statistics, Universidade de São Paulo, Rua do Matão 1010, CEP 05508-090, São Paulo, SP, Brazil.
∗∗ Postal address: Institute of Mathematics and Statistics, Universidade de São Paulo, Rua do Matão 1010, CEP 05508-090, São Paulo, SP, Brazil.
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Abstract

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We study four discrete-time stochastic systems on N, modeling processes of rumor spreading. The involved individuals can either have an active or a passive role, speaking up or asking for the rumor. The appetite for spreading or hearing the rumor is represented by a set of random variables whose distributions may depend on the individuals. Our goal is to understand - based on the distribution of the random variables - whether the probability of having an infinite set of individuals knowing the rumor is positive or not.

Keywords

Coverage of spaceepidemic modeldisk percolationrumor model

MSC classification

Secondary:60K35: Interacting random processes; statistical mechanics type models; percolation theory60G50: Sums of independent random variables; random walks

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 3 , September 2011, pp. 624 - 636
Copyright
Copyright © Applied Probability Trust 2011 

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