Ten Lectures on the Probabilistic Method: Second Edition

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SIAM, 1994 - Mathematics - 88 pages
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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.
  

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Contents

LECTURE 1 The Probabilistic Method
1
LECTURE 2 The Deletion Method and Other Refinements
11
LECTURES Random Graphs I
17
LECTURE 4 Large Deviations and Nonprobabilistic Algorithms
29
LECTURE 5 Discrepancy I
30
LECTURE 6 Chaos from Order
45
LECTURE 7 Random Graphs II
51
LECTURE 8 The Lovdsz Local Lemma
57
LECTURE 9 Discrepancy II
67
LECTURE 10 Six Standard Deviations Suffice
75
BONUS LECTURE The Janson Inequalities
81
INDEX
87
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