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How does breaking detailed balance accelerate convergence to equilibrium?

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SIN - Scalable inference; statistical, algorithmic, computational aspects

A number of recent results show that irreversible Markov chains (which lack detailed balance) tend to converge faster to their steady states, compared to reversible ones (where detailed balance holds).  We analyse this convergence in terms of large deviations of time-averaged quantities.  For interacting-particle systems which have hydrodynamic limits with diffusive behaviour, we present a geometrical interpretation of this acceleration, on the hydrodynamic scale [1].  We also discuss how this geometrical structure originates in the underlying (microscopic) Markov models.

[1] M Kaiser, RL Jack, and J Zimmer, “Acceleration of convergence to equilibrium in Markov chains by breaking detailed balance”, J. Stat. Phys., in press (2017).



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