逾滲（第2版）

《逾滲（第2版）》是2012年08月世界圖書出版公司出版的圖書，作者是（英）里密特。

基本介紹

• 書名：逾滲（第2版）
• 作者：（英）里密特
• ISBN：9787510046292
• 出版社：世界圖書出版公司
• 出版時間：2012年08月

內容簡介

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.Nor have I spent much time or space on the relationship of percolation to statistical physics，infinite particle systems，disordered media，reliability theory，and so on.With the exception of the two final chapters，I have tried to stay reasonably close to core material of the sort which most graduate students in the area might aspire to know.No critical reader will agree entirely with my selection，and physicists may sometimes feel that my intuition is crooked.

目錄

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