| Description |
1 online resource (v, 84 pages) |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; volume 232, number 1092 |
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Memoirs of the American Mathematical Society ; no. 1092.
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| 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 |
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Print version record |
| Subject |
Markov processes.
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Spin waves -- Mathematical models
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Markov processes
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Spin waves -- Mathematical models
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| Form |
Electronic book
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| Author |
Nachmias, Asaf, author
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Ning, Weiyang, author
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Peres, Y. (Yuval), author.
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American Mathematical Society, publisher
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| ISBN |
9781470418953 |
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1470418959 |
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