dc.contributor.advisor Hoffman, Christopher en_US dc.contributor.author Ning, Weiyang en_US dc.date.accessioned 2013-07-25T17:49:21Z dc.date.available 2013-07-25T17:49:21Z dc.date.issued 2013-07-25 dc.date.submitted 2013 en_US dc.identifier.other Ning_washington_0250E_11751.pdf en_US dc.identifier.uri http://hdl.handle.net/1773/23415 dc.description Thesis (Ph.D.)--University of Washington, 2013 en_US dc.description.abstract The 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.mimetype application/pdf en_US dc.language.iso en_US en_US dc.rights Copyright is held by the individual authors. en_US dc.subject.other Mathematics en_US dc.subject.other mathematics en_US dc.title Markov chain mixting time, card shuffling and spin systems dynamics en_US dc.type Thesis en_US dc.embargo.terms No embargo en_US
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