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Conference Papers Year : 2017

When Does Memory Speed-up Mixing?

Abstract

We investigate under which conditions a higher-order Markov chain, or more generally a Markov chain on an extended state space, can mix faster than a standard Markov chain on a graph of interest. We find that, depending on the constraints on the dynamics, two very different scenarios can emerge: under strict invariance of the target marginal and for general initialization of the lifted chain no speedup is possible; on the other hand, if these requirements are both relaxed, the lifted dynamics can achieve mixing in a time that corresponds to the diameter of the graph, which is optimal.
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Dates and versions

hal-01634630 , version 1 (14-11-2017)

Identifiers

  • HAL Id : hal-01634630 , version 1

Cite

Simon Apers, Alain Sarlette, Francesco Ticozzi. When Does Memory Speed-up Mixing?. IEEE Conference on Decision and Control, Dec 2017, Melbourne, Australia. ⟨hal-01634630⟩
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