The Probabilistic Method

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John Wiley & Sons, Apr 5, 2004 - Mathematics - 328 pages
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The leading reference on probabilistic methods in combinatorics-nowexpanded and updated

When it was first published in 1991, The Probabilistic Methodbecame instantly the standard reference on one of the most powerfuland widely used tools in combinatorics. Still without competitionnearly a decade later, this new edition brings you up to speed onrecent developments, while adding useful exercises and over 30% newmaterial. It continues to emphasize the basic elements of themethodology, discussing in a remarkably clear and informal styleboth algorithmic and classical methods as well as modernapplications.

The Probabilistic Method, Second Edition begins with basictechniques that use expectation and variance, as well as the morerecent martingales and correlation inequalities, then exploresareas where probabilistic techniques proved successful, includingdiscrepancy and random graphs as well as cutting-edge topics intheoretical computer science. A series of proofs, or "probabilisticlenses," are interspersed throughout the book, offering addedinsight into the application of the probabilistic approach. New andrevised coverage includes:
* Several improved as well as new results
* A continuous approach to discrete probabilistic problems
* Talagrand's Inequality and other novel concentrationresults
* A discussion of the connection between discrepancy andVC-dimension
* Several combinatorial applications of the entropy function andits properties
* A new section on the life and work of Paul Erdös-thedeveloper of the probabilistic method
 

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Contents

TOPICS
153
Bounding of Large Deviations
263
Trianglefree Graphs Have Large Independence Numbers
272
Paul Erdos
275
References
283
Subject Index
295
Author Index
299
Copyright

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Page ii - USA JAN KAREL LENSTRA Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands JOEL H.

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About the author (2004)

NOGA ALON, PhD, is a Baumritter Professor of Mathematics andComputer Science at Tel Aviv University. He is a member of theIsrael National Academy of Sciences and received the ErdösPrize in 1989, the Feher Prize in 1991, and the Polya Prize in2000.

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

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