Item description for Percolation (Grundlehren der mathematischen Wissenschaften) by Geoffrey R. Grimmett...
Percolation theory is the study of an idealized random medium in two or more dimensions. The mathematical theory is mature, and continues to give rise to problems of special beauty and difficulty. Percolation is pivotal for studying more complex physical systems exhibiting phase transitions. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most accessible proofs. The book is intended for graduate students and researchers in probability and mathematical physics. Almost no specialist knowledge is assumed. Much new material appears in this second edition, including: dynamic and static renormalization, strict inequalities between critical points, a sketch of the lace expansion, and several essays on related fields and applications.
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Est. Packaging Dimensions: Length: 9.5" Width: 6.2" Height: 1.1" Weight: 1.35 lbs.
Release Date Jun 11, 1999
ISBN 3540649026 ISBN13 9783540649021
Availability 57 units. Availability accurate as of May 25, 2017 10:00.
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More About Geoffrey R. Grimmett
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.
Geoffrey R. Grimmett has an academic affiliation as follows - University of Cambridge Statistical Laboratory, University of Cambridg.
Reviews - What do customers think about Percolation (Grundlehren der mathematischen Wissenschaften)?
Excellent Apr 26, 2000
The latest edition of Dr Grimmett's Percolation is surely the best book on the subject. He presents topics as clearly as possible without neglecting the technical details. His writing style is very readable, making much of this book accessible even to those who don't have all the necessary background in mathematics to understand all the proofs. Anyone looking for an easy introduction to the topic would be better off with Stauffer's book. But to gain any moderate understanding of this fascinating subject, and the methods and results of current research, this is the only book to have.
Percolation Apr 5, 2000
Grimmett's book, Percolation, is excellent.
Percolation theory began in the 50's; its mathematics is now quite mature, but the theory has recently acquired new techniques because many of the questions initially raised by percolation theory are still unanswered.
Percolation technology is now a cornerstone of the theory of disordered systems, and the methods of this book are now being extended into dynamical systems theory and the life sciences. This book covers the mathematics of percolation theory, presenting the shortest rigorous proofs of the main facts. Many problems in percolation theory are beautiful, but some of the apparent simplicity of the subject is deceiving, because the subject is quite deep. Grimmett cuts through many of the difficulties presenting the important concepts clearly and sucinctly.
The author restricts himself- for accessibility to the maximum readership-to bond percolation on a cubic lattice. Grimmett presents the core material at a graduate level for folks conversant with elementary probability theory and real analysis. Having some knowledge of ergodic theory, graph theory, and some mathematical physics helps, however. There is litle discussion of continuous, mixed, inhomogenous, long range, first passage or oriented percolation.
Beginning with existance of Psubc for the edge probability p we arrive at an infinite open cluster followed by discusssion of the basic techniques of the FKC, BK inequalities and Russo's formula. Grimmett then discusses open clusters per vertex and subcritical percolation, beginning with the Aizeman-Barsky and Menshikov methods for identifying the critical point, followed by a systematic study of the subcritical phase. He then discusses supercritical percolation, including 2 dimensional percolation, continuum percolation and random processes. The author gives a full list of references.