The Probabilistic Method

by Alon, Noga; Spencer, Joel H.

• ISBN13: 9780471722151
• ISBN10: 0471722154
• Edition: 2nd
• Format: eBook
• Copyright: 2005-02-07
• Publisher: Wiley-Interscience

Summary

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 Erd?s-the developer of the probabilistic method

Author Biography

NOGA ALON, PhD, is a Baumritter Professor of Mathematics and Computer Science at Tel Aviv University. He is a member of the Israel National Academy of Sciences and received the Erdos Prize in 1989, the Feher Prize in 1991, and the Polya Prize in 2000.

JOEL H. SPENCER, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of New York University. He is the cofounder and coeditor of the journal Random Structures and Algorithms and is also a Sloane Foundation Fellow.

Table of Contents

METHODS.

The Basic Method.

Linearity of Expectation.

Alterations.

The Second Moment.

The Local Lemma.

Correlation Inequalities.

Martingales and Tight Concentration.

The Poisson Paradigm.

Pseudo-Randomness.

TOPICS.

Random Graphs.

Circuit Complexity.

Discrepancy.

Geometry.

Codes, Games and Entropy.

Derandomization.

Appendices.

Indexes.

References.