Cutoff for the Swendsen-wang dynamics on the lattice

Danny Nam, Allan Sly

Research output: Contribution to journalArticle

Abstract

We study the Swendsen-Wang dynamics for the q-state Potts model on the lattice. Introduced as an alternative algorithm of the classical singlesite Glauber dynamics, the Swendsen-Wang dynamics is a nonlocal Markov chain that recolors many vertices at once based on the random-cluster representation of the Potts model. In this work, we establish cutoff phenomenon for the Swendsen-Wang dynamics on the lattice at sufficiently high temperatures, proving that it exhibits a sharp transition from "unmixed" to "well mixed." In particular, we show that at high enough temperatures the Swendsen-Wang dynamics on the torus (Z/nZ)d has cutoff at time (-log(1-γ)-1 log n, where γ (β) is the spectral gap of the infinitevolume dynamics.

Original languageEnglish (US)
Pages (from-to)3705-3761
Number of pages57
JournalAnnals of Probability
Volume47
Issue number6
DOIs
StatePublished - Jan 1 2019

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Cutoff phenomenon
  • Markov chains
  • Potts model
  • Swendsen-Wang dynamics

Fingerprint Dive into the research topics of 'Cutoff for the Swendsen-wang dynamics on the lattice'. Together they form a unique fingerprint.

  • Cite this