dc.contributor.author Hermon, J dc.contributor.author Peres, Y dc.date.accessioned 2018-03-16T15:15:03Z dc.date.available 2018-03-16T15:15:03Z dc.date.issued 2018 dc.identifier.issn 0178-8051 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/274054 dc.description.abstract There 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.publisher Springer Science and Business Media LLC dc.title A characterization of L2 mixing and hypercontractivity via hitting times and maximal inequalities dc.type Article prism.endingPage 800 prism.issueIdentifier 3-4 prism.publicationDate 2018 prism.publicationName Probability Theory and Related Fields prism.startingPage 769 prism.volume 170 dc.identifier.doi 10.17863/CAM.21135 rioxxterms.versionofrecord 10.1007/s00440-017-0769-x rioxxterms.version AM rioxxterms.licenseref.uri http://www.rioxx.net/licenses/all-rights-reserved rioxxterms.licenseref.startdate 2018-04-01 dc.contributor.orcid Hermon, Jonathan [0000-0002-2935-3999] dc.identifier.eissn 1432-2064 dc.publisher.url http://dx.doi.org/10.1007/s0044 rioxxterms.type Journal Article/Review cam.issuedOnline 2017-03-14 rioxxterms.freetoread.startdate 2018-03-14
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