Percolation

Erscheinungsjahr 2013
ISBN: 978-0-521-87232-4
Verlag: Cambridge University Press

Buch, Englisch, 334 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 636 g

Percolation theory was initiated some fifty years ago as a mathematical framework for the study of random physical processes such as flow through a disordered porous medium. It has proved to be a remarkably rich theory, with applications beyond natural phenomena to topics such as network modelling. The aims of this book are twofold. First to present classical results in a way that is accessible to non-specialists. Second, to describe, for the first time in a book, recent results of Smirnov in conformal invariance, and outline the proof that the critical probability for random Voronoi percolation in the plane is 1/2. Throughout, the presentation is streamlined, with elegant and straightforward proofs requiring minimal background in probability and graph theory. Numerous examples illustrate the important concepts and enrich the arguments. All-in-all, it will be an essential purchase for mathematicians, physicists, electrical engineers and computer scientists working in this exciting area.

Autoren/Hrsg.

Bollobás, Bela

Riordan, Oliver

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Naturwissenschaften Physik Physik Allgemein Geschichte der Physik
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Naturwissenschaften Physik Physik Allgemein Experimentalphysik
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

Preface; 1. Basic concepts; 2. Probabilistic tools; 3. Percolation on Z2 - the Harris-Kesten Theorem; 4. Exponential decay and critical probabilities - theorems of Menshikov and Aizenman & Barsky; 5. Uniqueness of the infinite open cluster and critical probabilities; 6. Estimating critical probabilities; 7. Conformal invariance - Smirnov's Theorem; 8. Continuum percolation; Bibliography; Index; List of notation.

Über Autor(innen)

Riordan, Oliver
Oliver Riordan is a Royal Society Research Fellow in the University of Cambridge and Research Fellow of Trinity College, Cambridge. In May 2000 he shared the prize for solving Christopher Monckton's Eternity Puzzle.

Bollobás, Bela
Béla Bollobás is a Senior Research Fellow at Trinity College, Cambridge and is the Jabie Hardin Chair of Excellence in Combinatorics at the University of Memphis. He has held visiting positions from Seattle to Singapore, from Brazil to Zurich. This is his eleventh book.