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
M´ 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 L´ 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.