Percolation

Geoffrey R. Grimmett (Autor)

Buch | Softcover

XIII, 447 Seiten

2010 | 2. Softcover reprint of hardcover 2nd ed. 1999
Springer Berlin (Verlag)
978-3-642-08442-3 (ISBN)

Artikel merken

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.

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.

Erscheint lt. Verlag	6.12.2010
Reihe/Serie	Grundlehren der mathematischen Wissenschaften
Zusatzinfo	XIII, 447 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	685 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	combinatorics • cubic lattice • Fields • lattice • Mathematica • Mathematical Physics • percolation • Physics • Probability • renormalization • Vertices
ISBN-10	3-642-08442-7 / 3642084427
ISBN-13	978-3-642-08442-3 / 9783642084423
Zustand	Neuware