Markov Chains and Mixing Times

ISBN-10: 0821847392
ISBN-13: 9780821847398
Edition: 2008
List price: $67.00
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Description: This text is an introduction to the modern approach to the theory of Markov chains. The main goals of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of  More...

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Book details

List price: $67.00
Copyright year: 2008
Publisher: American Mathematical Society
Publication date: 12/9/2008
Binding: Hardcover
Pages: 371
Size: 7.25" wide x 10.25" long x 1.00" tall
Weight: 1.672
Language: English

This text is an introduction to the modern approach to the theory of Markov chains. The main goals of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of the state space.

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 cut-off phenomenon
Lamplighter walks Continuous-time chains
Countable state-space chains
Coupling from the past Open problems
Notes on notation Appendix B: Background material
Introduction to simulation
Solutions to selected exercises
Bibliography
Index

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