dc.contributor.author Gheissari, Reza dc.date.accessioned 2017-10-11T15:36:43Z dc.date.available 2017-10-11T15:36:43Z dc.date.issued 2017-10-02 dc.identifier.uri http://hdl.handle.net/1853/58826 dc.description Presented on October 2, 2017 at 11:00 a.m. in the Klaus Advanced Computing Building, room 1116E. en_US dc.description Reza 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.description Runtime: 52:26 minutes en_US dc.description.abstract The 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. en_US 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 $q>4$. dc.format.extent 52:26 minutes dc.language.iso en_US en_US dc.relation.ispartofseries ARC Colloquium en_US dc.subject Markov chain en_US dc.subject Mixing time en_US dc.subject Potts model en_US dc.title Mixing Times of Critical 2D Potts Models en_US dc.type Lecture en_US dc.type Video en_US dc.contributor.corporatename Georgia Institute of Technology. Algorithms, Randomness and Complexity Center en_US dc.contributor.corporatename New York University. Dept. of Mathematics en_US
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