Percolation

Name: Percolation
Price: 84.29 USD
Availability: InStock
ISBN: 9780521872324

ISBN-10: 0521872324

ISBN-13: 9780521872324

Edition: 2006

Authors: Oliver Riordan, Bela Bollobï¿½s

List price: $105.00

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Description:

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…

Book details

List price: $105.00
Copyright year: 2006
Publisher: Cambridge University Press
Publication date: 9/21/2006
Binding: Hardcover
Pages: 334
Size: 6.34" wide x 9.25" long x 0.79" tall
Weight: 1.452
Language: English



Preface



Basic concepts and results



Probabilistic tools



Bond percolation on Z[superscript 2] - the Harris-Kesten Theorem



The Russo-Seymour-Welsh method



Harris's Theorem



A sharp transition



Kesten's Theorem



Dependent percolation and exponential decay



Sub-exponential decay



Exponential decay and critical probabilities - theorems of Menshikov and Aizenman & Barsky



The van den Berg-Kesten inequality and percolation



Oriented site percolation



Almost exponential decay of the radius - Menshikov's Theorem



Exponential decay of the radius



Exponential decay of the volume - the Aizenman-Newman Theorem



Uniqueness of the infinite open cluster and critical probabilities



Uniqueness of the infinite open cluster - the Aizenman-Kesten-Newman Theorem



The Harris-Kesten Theorem revisited



Site percolation on the triangular and square lattices



Bond percolation on a lattice and its dual



The star-delta transformation



Estimating critical probabilities



The substitution method



Comparison with dependent percolation



Oriented percolation on Z[superscript 2]



Non-rigorous bounds



Conformal invariance - Smirnov's Theorem



Crossing probabilities and conformal invariance



Smirnov's Theorem



Critical exponents and Schramm-Loewner evolution



Continuum percolation



The Gilbert disc model



Finite random geometric graphs



Random Voronoi percolation


Bibliography


Index


List of notation