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Probabilistic Method (Hardcover) (Noga Alon)
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This Fourth 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 aclear 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. This new edition features a new proof of the Local Lemma that provides an effective algorithm for finding desired objects. The authors have also added discussions on The Phase Transition (specifically a recent argument of Sudakov and Krivelevich, which proves the existence and uniqueness of the giant component) and Graph Limits (including new advances by Lovasz that provide a natural generalization of random graphs and limit the sequence of finite graphs). Various sections have also been updated to reflect recent research and advances, including Six Standard Deviations Suffice and Property B.