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A power law of order 1/4 for critical mean-field Swendsen-Wang dynamics | | Yun Long
; Asaf Nachmias
; Weiyang Ning
; Yuval Peres
; | | Date: |
15 Jul 2011 | | Abstract: | The Swendsen-Wang dynamics is a Markov chain widely used by physicists to
sample from the Boltzmann-Gibbs distribution of the Ising model. Cooper, Dyer,
Frieze and Rue proved that on the complete graph K_n the mixing time of the
chain is at most O(n^{1/2}) for all non-critical temperatures. In this paper we
show that the mixing time is Theta(1) in high temperatures, Theta(log n) in low
temperatures and Theta(n^{1/4}) at criticality. We also provide an upper bound
of O(log n) for Swendsen-Wang dynamics for the q-state ferromagnetic Potts
model on any tree with n vertices. | | Source: | arXiv, 1107.2970 | | Services: | Forum | Review | PDF | Favorites | |
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