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Behrends E. Introduction to Markov Chains: With Special Emphasis on Rapid Mixing

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Behrends E. Introduction to Markov Chains: With Special Emphasis on Rapid Mixing
Springer, 2000. — 237 p. — (Advanced Lectures in Mathematics). — ISBN 3528069864.
Besides the investigation of general chains the book contains chapters which are concerned with eigenvalue techniques, conductance, stopping times, the strong Markov property, couplings, strong uniform times, Markov chains on arbitrary finite groups (including a crash-course in harmonic analysis), random generation and counting, Markov random fields, Gibbs fields, the Metropolis sampler, and simulated annealing. With 170 exercises.
Contents
Finite Markov chains (the background)
Markov chains: how to start?
Exam.ples of Markov chains
How linear algebra comes into play
The fundamental not ions in connection with Markov chains
Transient states
An analytical lemma
Irreducible Markov chains
Notes and remarks
Rapidly mixing chains
Perron-Frobenius theory
Rapid mixing: a first approach
Conductance
Stopping times and the strong Markov property
Coupling methods
Strong uniform times
Markov chains on finite groups I (commutative groups)
Markov chains on finite groups 11 (arbitrary groups)
Notes and remarks
Rapidly mixing chains: applications
Random generation and counting
Markov random fields
Potentials, Gibbs fields, and the Ising model
The Metropolis sampier and simulated annealing
Notes and remarks
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