Population dynamics of surface-mediated autocatalytic processes (opens in new tab)

We investigate the population dynamics of surface-mediated autocatalytic processes, in which particles diffuse in a complex environment towards surface regions where they can be either killed or replicated. These opposite mechanisms compete with each other and lead to a sophisticated stochastic evolution of the population size. We provide a systematic analysis of the generating function of the population size. We also deduce its distribution, me...