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dc.contributor.authorGheissari, Reza
dc.date.accessioned2017-10-11T15:36:43Z
dc.date.available2017-10-11T15:36:43Z
dc.date.issued2017-10-02
dc.identifier.urihttp://hdl.handle.net/1853/58826
dc.descriptionPresented on October 2, 2017 at 11:00 a.m. in the Klaus Advanced Computing Building, room 1116E.en_US
dc.descriptionReza Gheissari is a 4th year mathematics PhD student at New York University's Courant Institute of Mathematical Sciences. His research interests are probability theory and statistical mechanics and statics and dynamics of spin systems.en_US
dc.descriptionRuntime: 52:26 minutesen_US
dc.description.abstractThe Potts model is a generalization of the Ising model to $q\geq 3$ states; on $\mathbb Z^d$ it is an extensively studied model of statistical mechanics, known to exhibit a rich phase transition for $d=2$ at some $\beta_c(q)$. Specifically, the Gibbs measure on $\mathbb Z^2$ exhibits a sharp transition between a disordered regime when $\beta<\beta_c(q)$ and an ordered regime when $\beta>\beta_c(q)$. At $\beta=\beta_c(q)$, when $q\leq 4$, the Potts model has a continuous phase transition and its scaling limit is believed to be conformally invariant; when $q>4$, the phase transition is discontinuous and the ordered and disordered phases coexist. I will discuss recent progress, joint with E. Lubetzky, in analyzing the time to equilibrium (mixing time) of natural Markov chains (e.g., heat-bath/Metropolis) for the 2D Potts model, where the mixing time on an $n\times n$ torus should transition from $O(\log n)$ at high temperatures to exponential in $n$ at low temperatures, via a critical slowdown at $\beta=\beta_c$ of $n^z$ when $q\leq 4$ and exponential in $n$ when $q>4$.en_US
dc.format.extent52:26 minutes
dc.language.isoen_USen_US
dc.relation.ispartofseriesARC Colloquiumen_US
dc.subjectMarkov chainen_US
dc.subjectMixing timeen_US
dc.subjectPotts modelen_US
dc.titleMixing Times of Critical 2D Potts Modelsen_US
dc.typeLectureen_US
dc.typeVideoen_US
dc.contributor.corporatenameGeorgia Institute of Technology. Algorithms, Randomness and Complexity Centeren_US
dc.contributor.corporatenameNew York University. Dept. of Mathematicsen_US


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