Georgia Institute of Technology College of Sciences

The Swendsen-Wang dynamics is a popular algorithm for sampling from the Gibbs distribution for the ferromagnetic Ising and Potts models. The dynamics is a global Markov chain that is conjectured to converge quickly to equilibrium even at low temperatures, where the correlations in the system are strong and local chains converge slowly. In this talk, we present new results concerning the speed of convergence of the Swendsen-Wang dynamics under spatial mixing (i.e., decay of correlations) conditions. In particular, we provide tight results for three distinct geometries: the integer d-dimensional integer lattice graph Z^d, regular trees, and random d-regular graphs. Our approaches crucially exploit the underlying geometry in different ways in each case.