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The Probabilistic Method, 2nd Edition

The Probabilistic Method, 2nd Edition

Noga Alon, Joel H. Spencer

ISBN: 978-0-471-72215-1 November 2004 328 Pages


The leading reference on probabilistic methods in combinatorics-now expanded and updated

When it was first published in 1991, The Probabilistic Method became instantly the standard reference on one of the most powerful and widely used tools in combinatorics. Still without competition nearly a decade later, this new edition brings you up to speed on recent developments, while adding useful exercises and over 30% new material. It continues to emphasize the basic elements of the methodology, discussing in a remarkably clear and informal style both algorithmic and classical methods as well as modern applications.

The Probabilistic Method, Second Edition begins with basic techniques that use expectation and variance, as well as the more recent martingales and correlation inequalities, then explores areas where probabilistic techniques proved successful, including discrepancy and random graphs as well as cutting-edge topics in theoretical computer science. A series of proofs, or "probabilistic lenses," are interspersed throughout the book, offering added insight into the application of the probabilistic approach. New and revised coverage includes:
* Several improved as well as new results
* A continuous approach to discrete probabilistic problems
* Talagrand's Inequality and other novel concentration results
* A discussion of the connection between discrepancy and VC-dimension
* Several combinatorial applications of the entropy function and its properties
* A new section on the life and work of Paul Erdös-the developer of the probabilistic method

The Basic Method.

Linearity of Expectation.


The Second Moment.

The Local Lemma.

Correlation Inequalities.

Martingales and Tight Concentration.

The Poisson Paradigm.



Random Graphs.

Circuit Complexity.



Codes, Games and Entropy.




" exciting well-written book which will give much enjoyment to a reader..." (Mathematical Reviews, 2003f)