On the behaviour of a rumour process with random stifling
arXiv:1004.1391 · doi:10.1016/j.envsoft.2010.10.015
Abstract
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.
12 pages, to appear in Environmental Modelling & Software