Markov chains and mixing times /
David A. Levin, Yuval Peres, Elizabeth L. Wilmer.
- xvii, 371 p. : ill. ; 26 cm.
'With a chapter on coupling from the past by James G. Propp and David B. Wilson.'
Includes bibliographical references (p. 353-361) and indexes.
Introduction to finite Markov chains -- Classical (and useful) Markov chains -- Markov chain Monte Carlo : metropolis and Glauber chains -- Introduction to Markov chain mixing -- Coupling -- Strong stationary times -- Lower bounds on mixing times -- The symmetric group and shuffling cards -- Random walks on networks -- Hitting times -- Cover times -- Eigenvalues -- Eigenfunctions and comparison of chains -- The transportation metric and path coupling -- The Ising model -- From shuffling cards to shuffling genes -- Martingales and evolving sets -- The cutoff phenomenon -- Lamplighter walks -- Continuous-time chains -- Countable state space chains -- Coupling from the past -- Open problems -- Appendix A : Background material -- Appendix B : Introduction to simulation.