Acknowledgements The authors thank the Mathematical Sciences Research Institute, the National Science Foundation VIGRE grant to the Department of Statistics at the University of California, Berkeley, and National Science Foundation grants DMS-0244479 and DMS-0104073 for support. We also thank Hugo Rossi for suggesting we embark on this project. Thanks to Blair Ahlquist, Tonci Antunovic, Elisa Celis, Paul Cuff, Jian Ding, Ori Gurel-Gurevich, Tom Hayes, Itamar Landau, Yun Long, Karola esz´ aros, Shobhana Murali, Weiyang Ning, Tomoyuki Shirai, Walter Sun, Sith- parran Vanniasegaram, and Ariel Yadin for corrections to an earlier version and making valuable suggestions. Yelena Shvets made the illustration in Section 6.5.4. The simulations of the Ising model in Chapter 15 are due to Raissa D’Souza. We thank aszl´ o Lov´ asz for useful discussions. We are indebted to Alistair Sinclair for his work co-organizing the M.S.R.I. program Probability, Algorithms, and Statisti- cal Physics in 2005, where work on this book began. We thank Robert Calhoun for technical assistance. Finally, we are greatly indebted to David Aldous and Persi Diaconis, who initi- ated the modern point of view on finite Markov chains and taught us much of what we know about the subject. xvii
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