The probabilistic method. 4th edition.

*(English)*Zbl 1333.05001
Wiley-Interscience Series in Discrete Mathematics and Optimization. Hoboken, NJ: John Wiley & Sons (ISBN 978-1-119-06195-3/hbk; 978-1-119-06207-3/ebook). 384 p. (2016).

Publisher’s description: Maintaining a standard of excellence that establishes this book as the leading reference on probabilistic methods in combinatorics, the fourth edition continues to feature a clear writing style, illustrative examples, and illuminating exercises. The new edition includes numerous updates to reflect the most recent developments and advances in discrete mathematics and the connections to other areas in mathematics, theoretical computer science, and statistical physics.

Emphasizing the methodology and techniques that enable problem-solving, the book begins with a description of tools applied to probabilistic arguments, includingbasic techniques that use expectation and variance as well as the more advanced applications ofmartingales and correlation inequalities. The authors explore where probabilistic techniques havebeen applied successfully and also examine topical coverage such as discrepancy and random graphs,circuit complexity, computational geometry, and derandomization of randomized algorithms. Written by two well-known authorities in the field, the fourth edition features:

See the reviews of the 1st, 2nd and 3rd editions in [Zbl 0767.05001; Zbl 0996.05001; Zbl 1148.05001].

Emphasizing the methodology and techniques that enable problem-solving, the book begins with a description of tools applied to probabilistic arguments, includingbasic techniques that use expectation and variance as well as the more advanced applications ofmartingales and correlation inequalities. The authors explore where probabilistic techniques havebeen applied successfully and also examine topical coverage such as discrepancy and random graphs,circuit complexity, computational geometry, and derandomization of randomized algorithms. Written by two well-known authorities in the field, the fourth edition features:

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- Additional exercises throughout with hints and solutions to select problems in an appendix to help readers obtain a deeper understanding of the best methods and techniques,
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- New coverage on topics such as the Local Lemma, Six Standard Deviations result in Discrepancy Theory, Property B, and graph limits,
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- Updated sections to reflect major developments on the newest topics, discussions of the hypergraph container method, and many new references and improved results.

See the reviews of the 1st, 2nd and 3rd editions in [Zbl 0767.05001; Zbl 0996.05001; Zbl 1148.05001].