Abstract

Given a finite strongly connected directed graph G = (V,E), we study a Markov chain taking values on the space of probability measures on V . The chain, motivated by biological applications in the context of stochastic population dynamics, is characterized by transitions between states that respect the structure superimposed by E: mass (probability) can only be moved between neighbors in G. We provide conditions for the ergodicity of the chain. In a simple, symmetric case, we fully characterize the invariant probability.