Geoffrey R. Grimmett

Percolation

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Grundlehren der mathematischen Wissenschaften 321
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-642-08442-3
• 2nd ed.
• Seitenzahl: 464
• Erscheinungstermin: 6. Dezember 2010
• Englisch
• Abmessung: 235mm x 155mm x 25mm
• Gewicht: 678g
• ISBN-13: 9783642084423
• ISBN-10: 3642084427
• Artikelnr.: 32058414

Autorenporträt

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.

Inhaltsangabe

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.