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Author Long, Yun, 1982- author.

Title A power law of order 1/4 for critical mean field Swendsen-Wang dynamics / Yun Long, Asaf Nachmias, Weiyang Ning, Yuval Peres
Published Providence, Rhode Island : American Mathematical Society, 2014


Description 1 online resource (v, 84 pages)
Series Memoirs of the American Mathematical Society, 0065-9266 ; volume 232, number 1092
Memoirs of the American Mathematical Society ; no. 1092.
Contents Chapter 1. Introduction Chapter 2. Statement of the results Chapter 3. Mixing time preliminaries Chapter 4. Outline of the proof of Theorem 2.1 Chapter 5. Random graph estimates Chapter 6. Supercritical case Chapter 7. Subcritical case Chapter 8. Critical Case Chapter 9. Fast mixing of the Swendsen-Wang process on trees Acknowledgements
Summary 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(\sqrt{n}) for all non-critical temperatures. In this paper the authors show that the mixing time is \Theta(1) in high temperatures, \Theta(\log n) in low temperatures and \Theta(n̂{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
Notes "Volume 232, Number 1092 (fourth of 6 numbers), November 2014."
Bibliography Includes bibliographical references (pages 83-84)
Notes English
Print version record
Subject Markov processes.
Spin waves -- Mathematical models
Markov processes
Spin waves -- Mathematical models
Form Electronic book
Author Nachmias, Asaf, author
Ning, Weiyang, author
Peres, Y. (Yuval), author.
American Mathematical Society, publisher
ISBN 9781470418953