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Seminar
FIELD Math:Analysis
DATE June 14 (Thu), 2018
TIME 14:00-15:30
PLACE 1424
SPEAKER Danny Nam
HOST Kang, Nam-Gyu
INSTITUTE Princeton
TITLE Cutoff phenomenon for the Swendsen-Wang dynamics
ABSTRACT

The Swendsen-Wang dynamics is an MCMC sampler of the Ising/Potts model, which recolors many vertices at once, as opposed to the classical single-site Glauber dynamics. Although widely used in practice due to efficiency, the mixing time of the Swendsen-Wang dynamics is far from being well-understood, mainly because of its non-local behavior.

In this talk, we prove cutoff phenomenon for the Swendsen-Wang dynamics on the lattice at high enough temperatures, meaning that the Markov chain exhibits a sharp transition from “unmixed” to “well-mixed.” The proof combines two earlier methods of proving cutoff, the update support [Lubetzky-Sly ’13] and information percolation [Lubetzky-Sly ’16], to establish cutoff in a non-local dynamics.

Joint work with Allan Sly.

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