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On the probability of rumour survival among sceptics

Part of: Markov processes Special processes

Published online by Cambridge University Press:  02 March 2023

Neda Esmaeeli Open the ORCID record for Neda Esmaeeli [Opens in a new window]  and
Farkhondeh Alsadat Sajadi
Neda Esmaeeli*
Affiliation:
University of Isfahan
Farkhondeh Alsadat Sajadi*
Affiliation:
University of Isfahan
*
*Postal address: Department of Applied Mathematics and Computer Science, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan 81746-73441, Iran. Email address: n.esmaeeli@sci.ui.ac.ir
**Postal address: Department of Statistics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan 81746-73441, Iran. Email address: f.sajadi@sci.ui.ac.ir
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Abstract

We study a sceptical rumour model on the non-negative integer line. The model starts with two spreaders at sites 0, 1 and sceptical ignorants at all other natural numbers. Then each sceptic transmits the rumour, independently, to the individuals within a random distance on its right after s/he receives the rumour from at least two different sources. We say that the process survives if the size of the set of vertices which heard the rumour in this fashion is infinite. We calculate the probability of survival exactly, and obtain some bounds for the tail distribution of the final range of the rumour among sceptics. We also prove that the rumour dies out among non-sceptics and sceptics, under the same condition.

Keywords

Rumour processrenewal processdouble coverage

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Type
Original Article
Information
Journal of Applied Probability , Volume 60 , Issue 3 , September 2023 , pp. 1096 - 1111
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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