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Cutoff for the Swendsen-Wang dynamics

Presented by: 
Danny Nam Princeton University, Seoul National University
Wednesday 18th July 2018 - 09:10 to 09:30
INI Seminar Room 1
The Swendsen-Wang dynamics is an MCMC sampler of the Ising/Potts model, which recolors many vertices at once based on the random-cluster representation of the model. 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 mixed€ to well-mixed.

Joint work with Allan Sly.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons