Title:
Spectral Independence in High-Dimensional Expanders and Applications to the Hardcore Model
Spectral Independence in High-Dimensional Expanders and Applications to the Hardcore Model
| dc.contributor.author | Liu, Kuikui | |
| dc.contributor.corporatename | Georgia Institute of Technology. Algorithms, Randomness and Complexity Center | en_US |
| dc.contributor.corporatename | University of Washington. School of Computer Science and Engineering | en_US |
| dc.date.accessioned | 2020-02-05T19:30:59Z | |
| dc.date.available | 2020-02-05T19:30:59Z | |
| dc.date.issued | 2020-01-27 | |
| dc.description | Presented on January 27, 2020 at 11:00 a.m. in the Groseclose Building, Room 402. | en_US |
| dc.description | Kuikui Liu is a second-year Ph.D. student in the Theory Group at the Paul G. Allen School for Computer Science and Engineering (UW CSE). He is advised by Professor Shayan Oveis Gharan. His research interests are in the geometry of polynomials, spectral graph theory, and high-dimensional geometry. He uses mathematical tools from these areas to design and analyze novel algorithms for solving hard problems. | en_US |
| dc.description | Runtime: 57:11 minutes | en_US |
| dc.description.abstract | We say a probability distribution µ is spectrally independent if an associated correlation matrix has a bounded largest eigenvalue for the distribution and all of its conditional distributions. We prove that if µ is spectrally independent, then the corresponding high dimensional simplicial complex is a local spectral expander. Using a line of recent works on mixing time of high dimensional walks on simplicial complexes [KM17; DK17; KO18; AL19], this implies that the corresponding Glauber dynamics mixes rapidly and generates (approximate) samples from µ. As an application, we show that natural Glauber dynamics mixes rapidly (in polynomial time) to generate a random independent set from the hardcore model up to the uniqueness threshold. This improves the quasi-polynomial running time of Weitz’s deterministic correlation decay algorithm [Wei06] for estimating the hardcore partition function, also answering a long-standing open problem of mixing time of Glauber dynamics [LV97; LV99; DG00; Vig01; Eft+16]. Joint work with Nima Anari and Shayan Oveis Gharan. | en_US |
| dc.format.extent | 57:11 minutes | |
| dc.identifier.uri | http://hdl.handle.net/1853/62422 | |
| dc.language.iso | en_US | en_US |
| dc.relation.ispartofseries | Algorithms and Randomness Center (ARC) Colloquium | |
| dc.subject | High dimensional | en_US |
| dc.subject | Spectral expander | en_US |
| dc.title | Spectral Independence in High-Dimensional Expanders and Applications to the Hardcore Model | 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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