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Catalogue Information
Field name	Details
Dewey Class	530.13
Title	Percolation ([EBook]) / by Geoffrey Grimmett.
Author	Grimmett, Geoffrey
Other name(s)	SpringerLink (Online service)
Edition statement	Second Edition.
Publication	Berlin, Heidelberg : Springer , 1999.
Physical Details	XIII, 447 pages : online resource.
Series	Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 0072-7830 ; ; 321
ISBN	9783662039816
Summary Note	Percolation theory is the study of an idealized random medium in two or more dimensions. It is a cornerstone of the theory of spatial stochastic processes with applications in such fields as statistical physics, epidemiology, and the spread of populations. Percolation plays a pivotal role in studying more complex systems exhibiting phase transition. The mathematical theory is mature, but continues to give rise to problems of special beauty and difficulty. 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 beyond undergraduate analysis and probability. This new volume differs substantially from the first edition through the inclusion of much new material, including: the rigorous theory of dynamic and static renormalization; a sketch of the lace expansion and mean field theory; the uniqueness of the infinite cluster; strict inequalities between critical probabilities; several essays on related fields and applications; numerous other results of significant. There is a summary of the hypotheses of conformal invariance. A principal feature of the process is the phase transition. The subcritical and supercritical phases are studied in detail. There is a guide for mathematicians to the physical theory of scaling and critical exponents, together with selected material describing the current state of the rigorous theory. To derive a rigorous theory of the phase transition remains an outstanding and beautiful problem of mathematics.:
Contents note	1 What is Percolation? -- 2 Some Basic Techniques -- 3 Critical Probabilities -- 4 The Number of Open Clusters per Vertex -- 5 Exponential Decay -- 6 The Subcritical Phase -- 7 Dynamic and Static Renormalization -- 8 The Supercritical Phase -- 9 Near the Critical Point: Scaling Theory -- 10 Near the Critical Point: Rigorous Results -- 11 Bond Percolation in Two Dimensions -- 12 Extensions of Percolation -- 13 Percolative Systems -- Appendix I. The Infinite-Volume Limit for Percolation -- Appendix II. The Subadditive Inequality -- List of Notation -- References -- Index of Names.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-662-03981-6
Links to Related Works	Subject References: Combinatorics . Mathematics . Percolation (Statistical physics) . Probabilities . Probability theory and stochastic processes . Theoretical, Mathematical and Computational Physics . Authors: Grimmett, Geoffrey . Corporate Authors: SpringerLink (Online service) . Series: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics . Classification: 530.13 . 530.13 (DDC) .

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Percolation

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