| eBook ISBN: | 978-1-4704-1895-3 |
| Product Code: | MEMO/232/1092.E |
| List Price: | $65.00 |
| MAA Member Price: | $58.50 |
| AMS Member Price: | $39.00 |
| eBook ISBN: | 978-1-4704-1895-3 |
| Product Code: | MEMO/232/1092.E |
| List Price: | $65.00 |
| MAA Member Price: | $58.50 |
| AMS Member Price: | $39.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 232; 2014; 84 ppMSC: Primary 60; Secondary 82
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 \(\Theta(n^{1/4})\) 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.
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Table of Contents
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Chapters
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1. Introduction
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2. Statement of the results
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3. Mixing time preliminaries
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4. Outline of the proof of Theorem
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5. Random graph estimates
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6. Supercritical case
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7. Subcritical case
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8. Critical Case
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9. Fast mixing of the Swendsen-Wang process on trees
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Acknowledgements
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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 \(\Theta(n^{1/4})\) 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.
-
Chapters
-
1. Introduction
-
2. Statement of the results
-
3. Mixing time preliminaries
-
4. Outline of the proof of Theorem
-
5. Random graph estimates
-
6. Supercritical case
-
7. Subcritical case
-
8. Critical Case
-
9. Fast mixing of the Swendsen-Wang process on trees
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Acknowledgements
