Percolation

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Percolation / Béla Bollobás, Oliver Riordan

資料種別:

図書

出版情報:

Cambridge : Cambridge University Press, c2006

形態:

x, 323 p. ; 24 cm

著者名:

ISBN:

9780521872324 [0521872324]

書誌ID:

BA78353647

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Includes bibliographical references and index

主題:

Percolation (Statistical physics)

言語:

英語

目次情報:

Preface

Basic concepts and results / 1：

Probabilistic tools / 2：

Bond percolation on Z[superscript 2] - the Harris-Kesten Theorem / 3：

The Russo-Seymour-Welsh method / 3.1：

Harris's Theorem / 3.2：

A sharp transition / 3.3：

Kesten's Theorem / 3.4：

Dependent percolation and exponential decay / 3.5：

Sub-exponential decay / 3.6：

Exponential decay and critical probabilities - theorems of Menshikov and Aizenman & Barsky / 4：

The van den Berg-Kesten inequality and percolation / 4.1：

Oriented site percolation / 4.2：

Almost exponential decay of the radius - Menshikov's Theorem / 4.3：

Exponential decay of the radius / 4.4：

Exponential decay of the volume - the Aizenman-Newman Theorem / 4.5：

Uniqueness of the infinite open cluster and critical probabilities / 5：

Uniqueness of the infinite open cluster - the Aizenman-Kesten-Newman Theorem / 5.1：

The Harris-Kesten Theorem revisited / 5.2：

Site percolation on the triangular and square lattices / 5.3：

Bond percolation on a lattice and its dual / 5.4：

The star-delta transformation / 5.5：

Estimating critical probabilities / 6：

The substitution method / 6.1：

Comparison with dependent percolation / 6.2：

Oriented percolation on Z[superscript 2] / 6.3：

Non-rigorous bounds / 6.4：

Conformal invariance - Smirnov's Theorem / 7：

Crossing probabilities and conformal invariance / 7.1：

Smirnov's Theorem / 7.2：

Critical exponents and Schramm-Loewner evolution / 7.3：

Continuum percolation / 8：

The Gilbert disc model / 8.1：

Finite random geometric graphs / 8.2：

Random Voronoi percolation / 8.3：

Bibliography

Index

List of notation

Preface

Basic concepts and results / 1：

Probabilistic tools / 2：

Bond percolation on Z[superscript 2] - the Harris-Kesten Theorem / 3：

The Russo-Seymour-Welsh method / 3.1：

Harris's Theorem / 3.2：

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