Ten Lectures on the Probabilistic Method (Cbms-Nsf Regional Conference Series in Applied Mathematics, No 52) - Softcover

Joel Spencer

Softcover

ISBN 10: 0898712130 ISBN 13: 9780898712131

Publisher: Society for Industrial & Applied Mathematics, 1987

Synopsis

This update of the 1987 title of the same name is an examination of what is currently known about the probabilistic method, written by one of its principal developers. Based on the notes from Spencer's 1986 series of ten lectures, this new edition contains an additional lecture: The Janson Inequalities. These inequalities allow accurate approximation of extremely small probabilities. A new algorithmic approach to the Lovasz Local Lemma, attributed to Jozsef Beck, has been added to Lecture 8, as well. Throughout the monograph, Spencer retains the informal style of his original lecture notes and emphasizes the methodology, shunning the more technical "best possible" results in favour of clearer exposition. The book is not encyclopaedic - it contains only those examples that clearly display the methodology. The probabilistic method is a powerful tool in graph theory, combinatorics, and theoretical computer science. It allows one to prove the existence of objects with certain properties (e.g., colourings) by showing that an appropriately defined random object has positive probability of having those properties. Spencer retains the informal style of his original lecture notes and emphasizes the methodology, shunning the more technical "best possible" results in favor of clearer exposition. Topics include: A description via examples of the basic Probabilistic Method and its refinements; Random Graphs; The Lovasz Local Lemma and its recent algorithmic implementations; Discrepancy; Derandomization; Large Deviation Estimates; Martingales; and the recent Janson Inequalities.

About this title

About the Author

Joel Spencer is professor of mathematics and computer science at Courant Institute, New York University.

Edition details

• Publisher: Society for Industrial & Applied Mathematics
• Publication date: 1987
• ISBN 10: 0898712130
• ISBN 13: 9780898712131
• Binding: Paperback
• Language: English