格里密特编著的《逾渗》内容介绍：This book is about the mathematics of percolation theory，with the emphasis upon presenting the shortest rigorous proofs of the main facts.I have made certain sacrifices in order to maximize the accessibility of the theory，and the major one has been to restrict myself almost entirely to the special case of bond percolation on the cubic lattice Zd.Thus there is only little discussion of such processes as continuum，mixed，inhomogeneous，long-range， first-passage，and oriented percolation.

1 What is Percolation？

 1.1 Modelling a Random Medium

 1.2 Why Percolation？

 1.3 Bond Percolation

 1.4 The Critical Phenomenon

 1.5 The Main Questions

 1.6 Site Percolation

 1.7 Notes

2 Some Basic Techniques

 2.1 Increasing Events

 2.2 The FKG Inequality

 2.3 The BK Inequality

 2.4 Russo's Formula

 2.5 Inequalities of Reliability Theory

 2.6 Another Inequality

 2.7 Notes

3 Critical Probabilities

 3.1 Equalities and Inequalities

 3.2 Strict Inequalities

 3.3 Enhancements

 3.4 Bond and Site Critical Probabilities

 3.5 Notes

4 The Number of Open Clusters per Vertex

 4.1 Definition

 4.2 Lattice Animals and Large Deviations

 4.3 Differentiability of K

 4.4 Notes

5 Exponential Decay

 5.1 Mean Cluster Size

 5.2 Exponential Decay of the Radius Distribution beneath Pe

 5.3 Using Differential Inequalities

 5.4 Notes

6 The Subcritical Phase

 6.1 The Radius of an Open Cluster

 6.2 Connectivity Functions and Correlation Length

 6.3 Exponential Decay of the Cluster Size Distribution

 6.4 Analyticity of K and X

 6.5 Notes

7 Dynamic and Static Renormalization

 7.1 Percolation in Slabs

 7.2 Percolation of Blocks

 7.3 Percolation in Half-Spaces

 7.4 Static Renormalization

 7.5 Notes

8 The Supercritical Phase

 8.1 Introduction

 8.2 Uniqueness of the Infinite Open Cluster

 8.3 Continuity of the Percolation Probability

 8.4 The Radius of a Finite Open Cluster

 8.5 Truncated Connectivity Functions and Correlation Length

 8.6 Sub-Exponential Decay of the Cluster Size Distribution

 8.7 Differentiability of

 8.8 Geometry of the Infinite Open Cluster

 8.9 Notes

9 Near the Critical Point： Scaling Theory

 9.1 Power Laws and Critical Exponents

 9.2 Scaling Theory

 9.3 Renormalization

 9.4 The Incipient Infinite Cluster

 9.5 Notes

10 Near the Critical Point：Rigorous Results

 10.1 Percolation on a Tree

 10.2 Inequalities for Critical Exponents

 10.3 Mean Field Theory

 10.4 Notes

11 Bond Percolation in Two Dimensions

12 Extensions of Percolation

13 Pereolative Systems

Appendix Ⅰ The Infinite-Volume Limit for Percolation

Appendix Ⅱ The Subadditive Inequality

List of Notation

References

Index of Names

Subject Index