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Mixing Times and Moving Targets

Published online by Cambridge University Press:  14 November 2013

PERLA SOUSI  and
PETER WINKLER
PERLA SOUSI
Affiliation:
DPMMS, University of Cambridge, Cambridge, UK (e-mail: p.sousi@statslab.cam.ac.uk)
PETER WINKLER
Affiliation:
Department of Mathematics, Dartmouth College, Hanover, NH 03755-3551, USA (e-mail: peter.winkler@dartmouth.edu)
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Abstract

We consider irreducible Markov chains on a finite state space. We show that the mixing time of any such chain is equivalent to the maximum, over initial states x and moving large sets (As)s, of the hitting time of (As)s starting from x. We prove that in the case of the d-dimensional torus the maximum hitting time of moving targets is equal to the maximum hitting time of stationary targets. Nevertheless, we construct a transitive graph where these two quantities are not equal, resolving an open question of Aldous and Fill on a ‘cat and mouse’ game.

Keywords

Primary 60J10Secondary 60J2760G40
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 23 , Issue 3 , May 2014 , pp. 460 - 476
Copyright
Copyright © Cambridge University Press 2013 

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References

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