On the behaviour of a rumour process with random stifling

Details On the behaviour of a rumour process with random stifling On the behaviour of a rumour process with random stifling

2010-04-08

arxiv.org/abs/1004.1391v2

Mathematics

Probability

12 pages, to appear in Environmental Modelling & Software

Scientific paper

10.1016/j.envsoft.2010.10.015

We propose a realistic generalization of the Maki-Thompson rumour model by assuming that each spreader ceases to propagate the rumour right after being involved in a random number of stifling experiences. We consider the process with a general initial configuration and establish the asymptotic behaviour (and its fluctuation) of the ultimate proportion of ignorants as the population size grows to $\infty$. Our approach leads to explicit formulas so that the limiting proportion of ignorants and its variance can be computed.

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