A power law of order 1/4 for critical mean field Swendsen-Wang dynamics
著者
書誌事項
A power law of order 1/4 for critical mean field Swendsen-Wang dynamics
（Memoirs of the American Mathematical Society, no. 1092）
American Mathematical Society, c2014
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注記
Other authors: Asaf Nachmias, Weiyang Ning, Yuval Peres
"Volume 232, number 1092 (fourth of 6 numbers), November 2014"
Includes bibliographical references (p. 83-84)
内容説明・目次
内容説明
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 Kn the mixing time of the chain is at most O(Ön) for all non-critical temperatures.
In this paper the authors show that the mixing time is Q(1) in high temperatures, Q(log n) in low temperatures and Q(n 1/4) at criticality. They also provide an upper bound of O(log n) for Swendsen-Wang dynamics for the q-state ferromagnetic Potts model on any tree of n vertices.
目次
Introduction
Statement of the results
Mixing time preliminaries
Outline of the proof of Theorem 2.1
Random graph estimates
Supercritical case
Subcritical case
Critical case
Fast mixing of the Swendsen-Wang process on trees
Acknowledgements
Bibliography
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