Overview
- Sequel to G. Grimmett's famous and influential book on Percolation (Grundlehren der mathematischen Wissenschaften 321)
- Author is leader in the field, and known as masterly expositor
- Includes some history of the subject from both mathematics and physics angles
- Includes supplementary material: sn.pub/extras
Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 333)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Reviews
From the reviews:
"This book constitutes an authoritative treatise of the random cluster model and its applications. It will be indispensable for anyone working on this and related subjects and can provide the basis for a graduate course or seminar." (Anton Bovier, Zentralblatt MATH, Vol. 1122 (24), 2007)
"This text is the first reference book devoted to the random-cluster model. The author knows the matter very well, since he is one of the first mathematicians who worked on this model. … This is a very useful book, because it is very well written and collects results that are currently disseminated in the literature." (Olivier Garet, Mathematical Reviews, Issue 2007 m)
"The random-cluster model was discovered in the late 1960s by P. W. Kasteleyn and his doctoral student C. M. Fortuin … . can be used in two ways: as an easily accessible introduction to the field for the newcomer, and as a valuable reference work of the present state of the art for the expert. The book is a must for anyone interested in percolation and mathematical Statistical Mechanics, and will certainly continue the success … ." (Hans-Otto Georgii, Combinatorics, Probability and Computing, Vol. 17, 2008)
"Readership: Probabilists, ranging from graduate students in general to experts on the random-cluster and related models. … The random-cluster model is a generalization of standard bond percolation. … In the random-cluster model, the probability distribution is perturbed by a factor q raised to the number of connected components. … The clarity of the exposition makes the book ideal for graduate students and other novices to the model." (Olle Häggström, International Statistical Review, Vol. 75 (2), 2007)
Authors and Affiliations
About the author
PhD (Oxford 1974) under supervision of John Hammersley and Dominic Welsh. Member of the Mathematics Department of Bristol University (1976-1992), and subsequently appointed to the Professorship of Mathematics Statistics at Cambridge University. Author of around 100 articles and five books in probability and related fields, including Percolation (Springer 1999), Probability and Random Processes (with David Stirzaker, Oxford University Press 2001). Managing Editor of "Probability Theory and Related Fields", 2001-2005.
Bibliographic Information
Book Title: The Random-Cluster Model
Authors: Geoffrey R. Grimmett
Series Title: Grundlehren der mathematischen Wissenschaften
DOI: https://doi.org/10.1007/978-3-540-32891-9
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2006
Hardcover ISBN: 978-3-540-32890-2Published: 13 June 2006
Softcover ISBN: 978-3-642-06943-7Published: 17 November 2010
eBook ISBN: 978-3-540-32891-9Published: 13 December 2006
Series ISSN: 0072-7830
Series E-ISSN: 2196-9701
Edition Number: 1
Number of Pages: XIII, 378
Topics: Probability Theory and Stochastic Processes, Theoretical, Mathematical and Computational Physics