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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