Toward a Theory of Markov Influence Systems and their Renormalization.
conference on innovations in theoretical computer science(2018)
摘要
Nonlinear chains are probabilistic models commonly used in physics, biology, and the social sciences. In Markov influence systems (MIS), the transition probabilities of the chains change as a function of the current state distribution. This work introduces a renormalization framework for analyzing the dynamics of MIS. It comes in two independent parts: first, we generalize the standard classification of chain states to the dynamic case by showing how to parse graph sequences. We then use this framework tocarry out the bifurcation analysis of a few important MIS families.In particular, we show that irreducible MIS are almost alwaysasymptotically periodic. We also give an example of hyper-torpid mixing, where a stationary distribution is reached in super-exponential time, a timescale that cannot be achieved by any chain.
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关键词
markov influence systems,renormalization,theory
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