Behrends Introduction to Markov Chains

With Special Emphasis on Rapid Mixing
Erscheinungsjahr 2014
ISBN: 978-3-322-90157-6
Verlag: Vieweg & Teubner
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 234 Seiten, eBook

Reihe: Advanced Lectures in Mathematics

The aims of this book are threefold: 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.

Behrends, Ehrhard

Inhaltsverzeichnis

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.

Über Autor(innen)

Prof. Dr. Ehrhard Behrends ist am Fachbereich Mathematik der Freien Universität Berlin tätig.