Show simple item record

dc.contributor.advisorHoffman, Christopheren_US
dc.contributor.authorNing, Weiyangen_US
dc.date.accessioned2013-07-25T17:49:21Z
dc.date.available2013-07-25T17:49:21Z
dc.date.issued2013-07-25
dc.date.submitted2013en_US
dc.identifier.otherNing_washington_0250E_11751.pdfen_US
dc.identifier.urihttp://hdl.handle.net/1773/23415
dc.descriptionThesis (Ph.D.)--University of Washington, 2013en_US
dc.description.abstractThe mixing time of a Markov chain describes how fast the Markov chain converges to its stationary distribution. In this thesis, we survey some of the knowledge and main tools available in this field by looking at examples. We focus on various models of card shuffling (random walk on the permutation group $S_n$) and the Swendsen-Wang dynamics of the mean-field Ising Model. We show that the Card-Cyclic to Random shuffle has mixing time of order $\Theta(n \log n)$ (joint work of Ben Morris and Yuval Peres). We also determine the order of the mixing time of the mean field Swendsen-Wang dynamics at all temperatures. In particular, at criticality, it mixes at time $\Theta(n^{1\over 4})$ (joint work of Yun Long, Asaf Nachmias, and Yuval Peres).en_US
dc.format.mimetypeapplication/pdfen_US
dc.language.isoen_USen_US
dc.rightsCopyright is held by the individual authors.en_US
dc.subject.otherMathematicsen_US
dc.subject.othermathematicsen_US
dc.titleMarkov chain mixting time, card shuffling and spin systems dynamicsen_US
dc.typeThesisen_US
dc.embargo.termsNo embargoen_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record