Percolation / Edition 2

by Geoffrey R. Grimmett

Overview

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.

Product Details

ISBN-13:	9783540649021
Publisher:	Springer Berlin Heidelberg
Publication date:	06/11/1999
Series:	Grundlehren der mathematischen Wissenschaften , #321
Edition description:	2nd ed. 1999
Pages:	447
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

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.

Editorial Reviews

"Percolation theory" springs from a model so simple (links dropped randomly onto a lattice) as to have applications to a remarkable variety of topics encountered in the pure and applied sciences. It motivates one to formulate questions which are easy to ask but (typically) formidably difficult to answer. Percolation theory is (like number theory) a fountainhead of good, meaty mathematical problems. In ten lively chapters the author provides luminous expert review of the present state of knowledge (and of ignorance) in the field. Good figures, historical and bibliographic notes, very attractively typeset, printed and bound. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)

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