A large deviations principle for the Maki–Thompson rumour model

We consider the stochastic model for the propagation of a rumour within a population which was formulated by Maki and Thompson [20]. Sudbury [22] established that, as the population size tends to infinity, the proportion of the population never hearing the rumour converges in probability to 0.2032. Watson [23] later derived the asymptotic normality of a suitably scaled version of this proportion. We prove a corresponding large deviations principle, with an explicit formula for the rate function.