Description 
1 online resource (v, 84 pages) 
Series 
Memoirs of the American Mathematical Society, 00659266 ; 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 SwendsenWang process on trees Acknowledgements 
Summary 
The SwendsenWang dynamics is a Markov chain widely used by physicists to sample from the BoltzmannGibbs 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 noncritical 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(nĚ‚{1/4}) at criticality. They also provide an upper bound of O(\log n) for SwendsenWang dynamics for the qstate 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 8384) 
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 

1470418959 
