Buch, Englisch, 234 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 474 g
With Special Emphasis on Rapid Mixing
Buch, Englisch, 234 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 474 g
Reihe: Advanced Lectures in Mathematics
ISBN: 978-3-528-06986-5
Verlag: Vieweg+Teubner Verlag
We start with a naive description of a Markov chain as a memoryless random walk on a finite set. This is complemented by a rigorous definition in the framework of probability theory, and then we develop the most important results from the theory of homogeneous Markov chains on finite state spaces.
Chains are called rapidly mixing if all of the associated walks, regardles of where they started, behave similarly already after comparitively few steps: it is impossible from observing the chain to get information on the starting position or the number of steps done so far. We will thoroughly study methods which have been proposed in the last decades to investigate this phenomenon.
A number of examples will be studied to indicate how the methods treated in this book can be applied.
Zielgruppe
Upper undergraduate
Autoren/Hrsg.
Weitere Infos & Material
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.
