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The Strange Logic of Random Graphs



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The study of random graphs was begun by Paul Erds 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... Read more
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Features
Author Joel H. Spencer
Format Hardcover
ISBN 9783540416548
Publication Date 26/12/2005
Publisher Springer
Manufacturer Springer-verlag Berlin And Heidelberg Gmbh & Co. K
Description

The study of random graphs was begun by Paul Erds 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.


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