#### Multiplex Markov Chains

##### Dane Taylor

Multiplex networks are a common modeling framework for interconnected systems and multimodal data, yet we still lack fundamental insights for how multiplexity affects stochastic processes. We introduce a "Markov chains of Markov chains" model such that with probably $(1-\omega)\in[0,1]$ random walkers remain in the same layer and follow (layer-specific) \emph{intralayer Markov chains}, whereas with probability $\omega$ they move to different layers following (node-specific) \emph{interlayer Markov chains}. By coupling "Markov-chain layers" versus "network layers", we identify novel multiplexity-induced phenomena including \emph{multiplex imbalance} (whereby the multiplex coupling of reversible Markov chains yields an irreversible one) and \emph{multiplex convection} (whereby a stationary distribution exhibits circulating flows that involve multiple layers). These phenomena (as well as the convergence rate $\lambda_2$) are found to exhibit optima for intermediate $\omega$, and we explore their relation to imbalances for the intralayer degrees of nodes. To provide analytical insight, we characterize stationary distributions for when there is timescale separation between transitions within and between layers (i.e., $\omega\to0$ and $\omega\to1$).

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