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Full Product Details

Author:   Geoffrey R. Grimmett
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of hardcover 1st ed. 2006
Volume:   333
Dimensions:   Width: 15.50cm , Height: 2.00cm , Length: 23.50cm
Weight:   0.605kg
ISBN:  

9783642069437

ISBN 10:   3642069436
Pages:   378
Publication Date:   17 November 2010
Audience:   Professional and scholarly ,  Professional & Vocational ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
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Table of Contents

Random-Cluster Measures.- Monotonic Measures.- Fundamental Properties.- Infinite-Volume Measures.- Phase Transition.- In Two Dimensions.- Duality in Higher Dimensions.- Dynamics of Random-Cluster Models.- Flows in Poisson Graphs.- On Other Graphs.- Graphical Methods for Spin Systems.

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 Haggstrom, International Statistical Review, Vol. 75 (2), 2007)

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 Haggstrom, International Statistical Review, Vol. 75 (2), 2007)

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 Haggstrom, International Statistical Review, Vol. 75 (2), 2007)

Author Information

"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."

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