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dc.contributor.authorHermon, J
dc.contributor.authorPeres, Y
dc.date.accessioned2018-03-16T15:15:03Z
dc.date.available2018-03-16T15:15:03Z
dc.date.issued2018
dc.identifier.issn0178-8051
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/274054
dc.description.abstractThere are several works characterizing the total-variation mixing time of a reversible Markov chain in term of natural probabilistic concepts such as stopping times and hitting times. In contrast, there is no known analog for the $L_{2}$ mixing time, $\tau_{2}$ (while there are sophisticated analytic tools to bound $ \tau_2$, in general they do not determine $\tau_2$ up to a constant factor and they lack a probabilistic interpretation). In this work we show that $\tau_2$ can be characterized up to a constant factor using hitting times distributions. We also derive a new extremal characterization of the Log-Sobolev constant, $c_{\mathrm{LS}}$, as a weighted version of the spectral gap. This characterization yields a probabilistic interpretation of $c_{\mathrm{LS}}$ in terms of a hitting time version of hypercontractivity. As applications of our results, we show that (1) for every reversible Markov chain, $\tau_2$ is robust under addition of self-loops with bounded weights, and (2) for weighted nearest neighbor random walks on trees, $\tau_2 $ is robust under bounded perturbations of the edge weights.
dc.publisherSpringer Science and Business Media LLC
dc.titleA characterization of L<inf>2</inf> mixing and hypercontractivity via hitting times and maximal inequalities
dc.typeArticle
prism.endingPage800
prism.issueIdentifier3-4
prism.publicationDate2018
prism.publicationNameProbability Theory and Related Fields
prism.startingPage769
prism.volume170
dc.identifier.doi10.17863/CAM.21135
rioxxterms.versionofrecord10.1007/s00440-017-0769-x
rioxxterms.versionAM
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserved
rioxxterms.licenseref.startdate2018-04-01
dc.contributor.orcidHermon, Jonathan [0000-0002-2935-3999]
dc.identifier.eissn1432-2064
dc.publisher.urlhttp://dx.doi.org/10.1007/s0044
rioxxterms.typeJournal Article/Review
cam.issuedOnline2017-03-14
rioxxterms.freetoread.startdate2018-03-14


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