Characterization of cutoff for reversible Markov chains
نویسندگان
چکیده
منابع مشابه
Characterization of cutoff for reversible Markov chains
A sequence of Markov chains is said to exhibit cutoff if the convergence to stationarity in total variation distance is abrupt. We prove a necessary and sufficient condition for cutoff in reversible lazy chains in terms of concentration of hitting time of certain sets of large stationary measure. (Previous works of Aldous, Oliviera, Sousi and the speaker established a less precise connection be...
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Natural mixing processes modeled by Markov chains often show a sharp cutoff in their convergence to long-time behavior. This paper presents problems where the cutoff can be proved (card shuffling, the Ehrenfests' urn). It shows that chains with polynomial growth (drunkard's walk) do not show cutoffs. The best general understanding of such cutoffs (high multiplicity of second eigenvalues due to ...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2017
ISSN: 0091-1798
DOI: 10.1214/16-aop1090