This Third Edition of The Probabilistic Method reflects the most recent developments in the field while maintaining the standard of excellence that established this book as the leading reference on probabilistic methods in combinatorics. Maintaining its clear writing style, illustrative examples, and practical exercises, this new edition emphasizes methodology, enabling readers to use probabilistic techniques for solving problems in such fields as theoretical computer science, mathematics, and statistical physics.
The book begins with a description of tools applied in probabilistic arguments, including basic techniques that use expectation and variance as well as the more recent applications of martingales and correlation inequalities. Next, the authors examine where probabilistic techniques have been applied successfully, exploring such topics as discrepancy and random graphs, circuit complexity, computational geometry, and derandomization of randomized algorithms. Sections labeled "The Probabilistic Lens" offer additional insights into the application of the probabilistic approach, and the appendix has been updated to include methodologies for finding lower bounds for Large Deviations.
The Third Edition also features:
- A new chapter on graph property testing, which is a current topic that incorporates combinatorial, probabilistic, and algorithmic techniques
- An elementary approach using probabilistic techniques to the powerful Szemeredi Regularity Lemma and its applications
- New sections devoted to percolation and liar games
- A new chapter that provides a modern treatment of the Erdos-Renyi phase transition in the Random Graph Process