Finite Markov Chains and Algorithmic Applications

by Olle Häggström

Overview

This text is ideal for advanced undergraduate or beginning graduate students. The author first develops the necessary background in probability theory and Markov chains before using it to study a range of randomized algorithms with important applications in optimization and other problems in computing. The book will appeal not only to mathematicians, but to students of computer science who will discover much useful material. This clear and concise introduction to the subject has numerous exercises that will help students to deepen their understanding.

Product Details

ISBN-13:	9780521890014
Publisher:	Cambridge University Press
Publication date:	05/30/2002
Series:	London Mathematical Society Student Texts , #52
Edition description:	New Edition
Pages:	126
Product dimensions:	6.02(w) x 8.98(h) x 0.31(d)

Table of Contents

1. Basics of probability theory; 2. Markov chains; 3. Computer simulation of Markov chains; 4. Irreducible and aperiodic Markov chains; 5. Stationary distributions; 6. Reversible Markov chains; 7. Markov chain Monte Carlo; 8. Fast convergence of MCMC algorithms; 9. Approximate counting; 10. Propp-Wilson algorithm; 11. Sandwiching; 12. Propp-Wilson with read once randomness; 13. Simulated annealing; 14. Further reading.

Editorial Reviews

"...extremely elegant...I am sure that students will find great pleasure in using the book—and that teachers will have the same pleasure in using it to prepare a course on the subject." Mathematics of Computation

"Here Haggstrom takes the beginning student from the first definitions concerning Markov chains even beyond Propp-Wilson to its refinementss and applications, all in just a hundred or so generously detailed pages. If an undergraduate reading this book comes away saying "I should have thought of that!" then the psychological barrier between school mathematics and research will have begun to break down. Few mathematical monographs provide a comparable opportunity. General readers; lower-division undergraduates through professionals." Choice

"[This series] is generally good....The use of examples to introduce the various algorithms is especially effective and makes the text easier to read." Mathematical Reviews

"The numerous examples perfectly well illustrate the more theoretical points. I am sure that students will find great pleasure in using the book-and that teachers will have the same pleasure in using it to prepare a course on the subject." Mathematics of Computation

From the Publisher

Based on a lecture course given at Chalmers University of Technology, this book is suitable for advanced undergraduate and beginning graduate students in statistics and computer science, and for mathematicians. Necessary background in probability theory and Markov chains is developed, then applied to the study of a range of randomized algorithms with applications on optimization and other problems in computing. Algorithms covered are the Markov chain Monte Carlo method, simulated annealing, and the recently developed Propp- Wilson algorithm. Annotation c. Book News, Inc., Portland, OR (booknews.com)