Items related to The Random-Cluster Model: 333 (Grundlehren der mathematische...
Synopsis
The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems. The book includes treatment of the first-order (discontinuous) phase transition.
"synopsis" may belong to another edition of this title.
Review
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)
From the Back Cover
The random-cluster model has emerged in recent years as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. This systematic study includes accounts of the subcritical and supercritical phases, together with clear statements of important open problems. There is an extensive treatment of the first-order (discontinuous) phase transition, as well as a chapter devoted to applications of the random-cluster method to other models of statistical physics.
"About this title" may belong to another edition of this title.
- PublisherSpringer
- Publication date2010
- ISBN 10 3642069436
- ISBN 13 9783642069437
- BindingPaperback
- LanguageEnglish
- Number of pages391
Buy New
View this item
£ 80.62
£ 15.49 shipping from United Kingdom to U.S.A.
Destination, rates & speeds
Search results for The Random-Cluster Model: 333 (Grundlehren der mathematische...
Stock Image
The Random-Cluster Model
Seller: Chiron Media, Wallingford, United Kingdom
Seller rating 5 out of 5 stars
PF. Condition: New. Seller Inventory # 6666-IUK-9783642069437
Quantity: 10 available
Stock Image
The Random-Cluster Model (Grundlehren der mathematischen Wissenschaften, 333)
Seller: Ria Christie Collections, Uxbridge, United Kingdom
Seller rating 5 out of 5 stars
Condition: New. In. Seller Inventory # ria9783642069437_new
Quantity: Over 20 available
Seller Image
The Random-Cluster Model
Published by
Springer Berlin Heidelberg Nov 2010, 2010
ISBN 10: 3642069436
ISBN 13: 9783642069437
New
Taschenbuch
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Germany
Seller rating 5 out of 5 stars
Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems. The book includes treatment of the first-order (discontinuous) phase transition. 396 pp. Englisch. Seller Inventory # 9783642069437
Quantity: 2 available
Seller Image
The Random-Cluster Model
Published by
Springer Berlin Heidelberg, 2010
ISBN 10: 3642069436
ISBN 13: 9783642069437
New
Taschenbuch
Seller: AHA-BUCH GmbH, Einbeck, Germany
Seller rating 5 out of 5 stars
Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - Therandom-clustermodelwasinventedbyCees[Kees]FortuinandPietKasteley n around 1969 as a uni cation of percolation, Ising, and Potts models, and as an extrapolation of electrical networks. Their original motivation was to harmonize the series and parallel laws satis ed by such systems. In so doing, they initiated a study in stochastic geometry which has exhibited beautiful structure in its own right, and which has become a central tool in the pursuit of one of the oldest challenges of classical statistical mechanics, namely to model and analyse the ferromagnet and especially its phase transition. The importance of the model for probability and statistical mechanics was not fully recognized until the late 1980s. There are two reasons for this period of dormancy. Although the early publications of 1969-1972 contained many of the basic properties of the model, the emphasis placed there upon combinatorial aspects may have obscured its potential for applications. In addition, many of the geometrical arguments necessary for studying the model were not known prior to 1980, but were developed during the 'decade of percolation' that began 1 then. In 1980 was published the proof that p = for bond percolation on the c 2 square lattice, and this was followed soon by Harry Kesten's monograph on t- dimensionalpercolation. Percolationmovedintohigherdimensionsaround1986, and many of the mathematical issues of the day were resolved by 1989. Interest in the random-cluster model as a tool for studying the Ising/Potts models was rekindled around 1987. Seller Inventory # 9783642069437
Quantity: 1 available
Stock Image
The Random-Cluster Model (Grundlehren der mathematischen Wissenschaften, 333)
Seller: California Books, Miami, FL, U.S.A.
Seller rating 5 out of 5 stars
Condition: New. Seller Inventory # I-9783642069437
Quantity: Over 20 available
Seller Image
The Random-Cluster Model
Published by
Springer Berlin Heidelberg, 2010
ISBN 10: 3642069436
ISBN 13: 9783642069437
New
Softcover
Seller: moluna, Greven, Germany
Seller rating 5 out of 5 stars
Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 expositorIncludes some history of the subject from both mathematics a. Seller Inventory # 5046029
Quantity: Over 20 available
Stock Image
The Random-Cluster Model
Seller: Revaluation Books, Exeter, United Kingdom
Seller rating 5 out of 5 stars
Paperback. Condition: Brand New. 380 pages. 8.90x5.90x1.30 inches. In Stock. Seller Inventory # x-3642069436
Quantity: 2 available
Stock Image
The Random-Cluster Model (Grundlehren der mathematischen Wissenschaften, 333)
Seller: Mispah books, Redhill, SURRE, United Kingdom
Seller rating 4 out of 5 stars
Paperback. Condition: Like New. Like New. book. Seller Inventory # ERICA79036420694366
Quantity: 1 available