Mathematics – Probability
Scientific paper
2012-01-27
Mathematics
Probability
17 pages
Scientific paper
We prove that the spectral gap of the Swendsen-Wang dynamics for the random-cluster model is larger than the spectral gap of a single-bond dynamics, that updates only a single edge per step. For this we give a representation of the algorithms on the joint (Potts/random-cluster) model. Furthermore we obtain upper and lower bounds on the mixing time of the single-bond dynamics on the discrete d-dimensional torus of side length L at the Potts transition temperature for $q$ large enough that are exponential in L^{d-1}, complementing a result of Borgs, Chayes and Tetali.
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