We develop a framework that allows us to define a hierarchy of approximations to the stationary distribution of general systems that can be described as discrete Markov processes with time invariant transition probabilities and (possibly) a large number of states. This results in an efficient method for studying social and biological communities in the presence of stochastic effects—such as mutations in evolutionary dynamics and a random exploration of choices in social systems—including situations where the dynamics encompasses the existence of stable polymorphic configurations, thus overcoming the limitations of existing methods. The present formalism is shown to be general in scope, widely applicable, and of relevance to a variety of interdisciplinary problems.
Recommended citation: Vítor V. Vasconcelos, Fernando P. Santos, Francisco C. Santos, and Jorge M. Pacheco. “Stochastic Dynamics through Hierarchically Embedded Markov Chains” Phys. Rev. Let. (2017) 118 058301