UID:
almahu_9947363411002882
Format:
X, 168 p.
,
online resource.
ISBN:
9783662045381
Series Statement:
Algorithms and Combinatorics, 22
Content:
The study of random graphs was begun by Paul Erdos and Alfred Renyi in the 1960s and now has a comprehensive literature. A compelling element has been the threshold function, a short range in which events rapidly move from almost certainly false to almost certainly true. This book now joins the study of random graphs (and other random discrete objects) with mathematical logic. The possible threshold phenomena are studied for all statements expressible in a given language. Often there is a zero-one law, that every statement holds with probability near zero or near one. The methodologies involve probability, discrete structures and logic, with an emphasis on discrete structures. The book will be of interest to graduate students and researchers in discrete mathematics.
Note:
I. Beginnings -- 0. Two Starting Examples -- 1. Preliminaries -- 2. The Ehrenfeucht Game -- II. Random Graphs -- 3. Very Sparse Graphs -- 4. The Combinatorics of Rooted Graphs -- 5. The Janson Inequality -- 6. The Main Theorem -- 7. Countable Models -- 8. Near Rational Powers of n -- III. Extras -- 9. A Dynamic View -- 10. Strings -- 11. Stronger Logics -- 12. Three Final Examples.
In:
Springer eBooks
Additional Edition:
Printed edition: ISBN 9783642074998
Language:
English
DOI:
10.1007/978-3-662-04538-1
URL:
http://dx.doi.org/10.1007/978-3-662-04538-1
URL:
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