The Probabilistic Method

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John Wiley & Sons, 20 sep. 2011 - 376 pagina's
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Praise for the Second Edition:

"Serious researchers in combinatorics or algorithm design will wish to read the book in its entirety...the book may also be enjoyed on a lighter level since the different chapters are largely independent and so it is possible to pick out gems in one's own area..."
Formal Aspects of Computing

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.

The Third Edition also features:

  • A new chapter on graph property testing, which is a current topic that incorporates combinatorial, probabilistic, and algorithmic techniques

  • An elementary approach using probabilistic techniques to the powerful Szemerédi Regularity Lemma and its applications

  • New sections devoted to percolation and liar games

  • A new chapter that provides a modern treatment of the Erdös-Rényi phase transition in the Random Graph Process

Written by two leading authorities in the field, The Probabilistic Method, Third Edition is an ideal reference for researchers in combinatorics and algorithm design who would like to better understand the use of probabilistic methods. The book's numerous exercises and examples also make it an excellent textbook for graduate-level courses in mathematics and computer science.

 

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Inhoudsopgave

PREFACE
2
Linearity of Expectation 2 1 Basics 2 2 Splitting Graphs 2 3 Two Quickies
The Second Moment
The Local
6
Martingales and Tight Concentration
8
Theory
Circuit Complexity
Discrepancy
Geometry
15
Derandomization
Graph Property Testing
Boundingof Large Deviations

Pseudorandomness
Random Graphs
The ErdösRényi Phase Transition

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Over de auteur (2011)

NOGA ALON, PhD, is Baumritter Professor of Mathematics and Computer Science at Tel Aviv University, Israel. A member of the Israel National Academy of Sciences, Dr. Alon has written over 400 published papers, mostly in the areas of combinatorics and theoretical computer science. He is the recipient of numerous honors in the field, including the Erdös Prize (1989), the Pólya Prize (2000), the Landau Prize (2005), and the Gödel Prize (2005).

JOEL H. SPENCER, PhD, is Professor of Mathematics and Computer Science at the Courant Institute of Mathematical Sciences at New York University and is the cofounder and coeditor of the journal Random Structures and Algorithms. Dr. Spencer has written over 150 published articles and is the coauthor of Ramsey Theory, Second Edition, also published by Wiley.

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