Swendsen--Wang Is Faster than Single-Bond Dynamics
نویسندگان
چکیده
منابع مشابه
Swendsen-Wang is faster than single-bond dynamics
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-d...
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We prove comparison results for the Swendsen-Wang (SW) dynamics, the heat-bath (HB) dynamics for the Potts model and the single-bond (SB) dynamics for the randomcluster model on arbitrary graphs. In particular, we prove that rapid (i.e. polynomial) mixing of HB implies rapid mixing of SW on graphs with bounded maximum degree and that rapid mixing of SW and rapid mixing of SB are equivalent. Add...
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Swendsen–Wang dynamics for the Potts model was proposed in the late 1980’s as an alternative to single-site heat-bath dynamics, in which global updates allow this MCMC sampler to switch between metastable states and ideally mix faster. Gore and Jerrum (1999) found that this dynamics may in fact exhibit slow mixing: they showed that, for the Potts model with q ≥ 3 colors on the complete graph on...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2014
ISSN: 0895-4801,1095-7146
DOI: 10.1137/120864003