The Random-Cluster Model by Geoffrey R Grimmett

The Random-Cluster Model by Geoffrey R Grimmett

The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems.

From the reviews:

"This book constitutes an authoritative treatise of the random cluster model and its applicationsIt 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)

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.

SKU	Unavailable
ISBN 13	9783642069437
ISBN 10	3642069436
Title	The Random-Cluster Model
Author	Geoffrey R Grimmett
Series	Grundlehren Der Mathematischen Wissenschaften
Condition	Unavailable
Binding Type	Paperback
Publisher	Springer
Year published	2010-11-17
Number of pages	378
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
Note	Unavailable