Title:
A characterization of $L_p$ mixing, cutoff and hypercontractivity via maximal inequalities and hitting times
A characterization of $L_p$ mixing, cutoff and hypercontractivity via maximal inequalities and hitting times
| dc.contributor.author | Hermon, Jonathan | |
| dc.contributor.corporatename | Georgia Institute of Technology. Algorithms, Randomness and Complexity Center | en_US |
| dc.contributor.corporatename | University of Cambridge. Dept. of Pure Mathematics and Mathematical Statistics | en_US |
| dc.date.accessioned | 2017-12-21T01:12:43Z | |
| dc.date.available | 2017-12-21T01:12:43Z | |
| dc.date.issued | 2017-11-27 | |
| dc.description | Presented on November 27, 2017 at 11:00 a.m. in the Klaus Advanced Computing Building, Room 1116E. | en_US |
| dc.description | Jonathan Hermon is a researcher in the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. His research interests are concentrated on problems in discrete probability theory with a special emphasis on problems related to the theory of mixing times of Markov chains and the cutoff phenomenon. | en_US |
| dc.description | Runtime: 56:54 minutes | en_US |
| 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 uniform ($L_{\infty}$) mixing time (UMT), (there is neither a sharp bound nor one possessing a probabilistic interpretation). We show that the UMT can be characterized up to a constant factor using hitting times distributions. We also derive a new extremal characterization of the Log-Sobolev constant, $c_{LS}$, as a weighted version of the spectral gap. This characterization yields a probabilistic interpretation of $c_{LS}$ in terms of a hitting time version of hypercontractivity. As applications, we (1) resolve a conjecture of Kozma by showing that the UMT is not robust under rough isometries (even in the bounded degree, unweighted setup), (2) show that for weighted nearest neighbor random walks on trees, the UMT is robust under bounded perturbations of the edge weights, and (3) Establish a general robustness result under addition of weighted self-loops. | en_US |
| dc.format.extent | 56:54 minutes | |
| dc.identifier.uri | http://hdl.handle.net/1853/59095 | |
| dc.language.iso | en_US | en_US |
| dc.relation.ispartofseries | Algorithms and Randomness Center (ARC) Colloquium | |
| dc.subject | Cutoff | en_US |
| dc.subject | Hitting-times | en_US |
| dc.subject | Mixing-times | en_US |
| dc.title | A characterization of $L_p$ mixing, cutoff and hypercontractivity via maximal inequalities and hitting times | en_US |
| dc.type | Moving Image | |
| dc.type.genre | Lecture | |
| dspace.entity.type | Publication | |
| local.contributor.corporatename | Algorithms and Randomness Center | |
| local.contributor.corporatename | College of Computing | |
| local.relation.ispartofseries | ARC Colloquium | |
| relation.isOrgUnitOfPublication | b53238c2-abff-4a83-89ff-3e7b4e7cba3d | |
| relation.isOrgUnitOfPublication | c8892b3c-8db6-4b7b-a33a-1b67f7db2021 | |
| relation.isSeriesOfPublication | c933e0bc-0cb1-4791-abb4-ed23c5b3be7e |
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