Multiplex Markov chains: Convection cycles and optimality

This paper proposes a multiplex generalization of Markov chains, whereby a set of Markov chain layers is coupled by a set of interlayer Markov chains. The resulting system gives rise to emergent convection cycles that are optimized, along with the convergence rate, when the transition probabilities within and between layers are balanced. The authors support these findings with spectral perturbation theory and an empirical study of frequency-multiplexed brain-activity data.