Alon N., Spencer J.H. The Probabilistic Method

3rd ed. — Wiley, 2008. — 373 p. — (Wiley-Interscience Series in Discrete Mathematics and Optimization). — ISBN: 978-0470170205.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.Methods.
The Basic Method.
Linearity of Expectation.
Alterations.
The Second Moment.
The Local Lemma.
Correlation Inequalities.
Martingales and Tight Concentration.
The Poisson Paradigm.
Pseudorandomness.Topics.Random Graphs.
The Erd" osR.
Circuit Complexity.
Discrepancy.
Geometry.
Codes, Games and Entropy.
Derandomization.
Graph Property Testing.Appendix A: Bounding of Large Deviations.
Appendix B: Paul Erd" os.