Eyal Lubetzky : Mixing times of critical Potts models (Mar 2, 2017 3:10 PM)

We will discuss recent progress, jointly with R. Gheissari, on the dynamical phase transition for the critical q-state Potts model on the 2D torus (both single-site dynamics such as Glauber/Metropolis and cluster dynamics such as Swendsen--Wang), where the conjectured behavior was a mixing time that is polynomial in the side-length for $q = 2,3,4$ colors but exponential in it for $q>4$. We will then present a proof from a recent work with R. Gheissari and Y. Peres, that, on the complete graph on $n$ vertices with $q>2$ colors, the Swendsen--Wang dynamics is exponentially slow in $n$, improving on the lower bound of $\exp(c\sqrt{n})$ due to Gore and Jerrum in 1999. If time permits, we will then revisit the model on the 2D lattice, and describe the effect of different boundary conditions on its dynamical behavior at criticality.

• Category: Probability
• Duration: 01:34:45
• Date:  March 2, 2017 at 3:10 PM
• Views: 114
• Tags:   seminar, Probability Seminar