Discrete Probability Models and Methods Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding

by Pierre Bremaud

Part of the Probability Theory and Stochastic Modelling Series

Discrete Probability Models and Methods Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding Synopsis

The emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale methods, the method of types) and versatile tools (Chernoff's bound, Hoeffding's inequality, Holley's inequality) whose domain of application extends far beyond the present text. Although the examples treated in the book relate to the possible applications, in the communication and computing sciences, in operations research and in physics, this book is in the first instance concerned with theory. The level of the book is that of a beginning graduate course. It is self-contained, the prerequisites consisting merely of basic calculus (series) and basic linear algebra (matrices). The reader is not assumed to be trained in probability since the first chapters give in considerable detail the background necessary to understand the rest of the book.

Discrete Probability Models and Methods Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and Coding Press Reviews

This is a book that any discrete proababilist will want to have on the shelf. It is a comprehensive extension of the author's masterfully written text Markov Chains ... Surprisingly; the book contains an extensive amount of information theory. ... In my opinion the new book would be ideal for a year-long course on discrete probability. (Yevgeniy Kovchegov, Mathematical Reviews, May, 2018) This is a comprehensive volume on the application of discrete probability to combinatorics, information theory, and related fields. It is accessible for first-year graduate students. ... Results are easy to find and reasonably easy to understand. ... Summing Up: Recommended. Graduate students and faculty. (M. Bona, Choice, Vol. 54 (12), August, 2017)

Book Information

ISBN: 9783319434759
Publication date: 3rd February 2017
Author: Pierre Bremaud
Publisher: Springer International Publishing AG
Format: Hardback
Pagination: 559 pages
Categories: Probability & statistics,

About Pierre Bremaud

Pierre Bremaud obtained his Doctorate in Mathematics from the University of Paris VI and his PhD from the department of Electrical Engineering and Computer Science of the University of California at Berkeley. He is a major contributor to the theory of stochastic processes and their applications, and has authored or co-authored several reference or textbooks on the subject.

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