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内容简介

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.

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目录

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

前言/序言

逾渗（第2版）（英文版） [Percolation] 电子书 下载 mobi epub pdf txt

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帮别人买得，还没来得及看，说是不错。

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逾渗理论是处理强无序和具有随机几何结构系统常用的理论方法之一。这一理论的研究中心内容是：当系统的成分或某种意义上的密度变化达到一定值（称为逾渗阈值）时，在逾渗阈值处系统的一些物理性质会发生尖锐的变化，即在逾渗阈值处，系统的一些物理现象的连续性会消失（而从另一方面看，则是突然出现）。 逾渗转变，指的是在庞大无序系统中随着联结程度，或某种密度、占据数、浓度的增加（或减少）到一定程度，系统内突然出现（或消失）某种长程联结性，性质发生突变，我们称发生了逾渗转变，或者说发生了尖锐的相变。正是这种逾渗转变，使之成为描述多种不同现象的一个自然模型，用于阐明相变和临界现象的一些最重要的物理概念，其中许多概念对非晶态固体（高分子材料是典型的一种）是十分有用的。逾渗理论的重要实际意义，在于它可广泛应用于说明众多物理、化学、生物及社会现象，迄今其应用范围还在不断扩大。表5-1列举了十五种不同的现象，都是已采用逾渗模型加以分析的。

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表1中约一半属宏观现象，一半属微观过程。宏观和微观的分界线在表的中间。这儿特意把两种极端情形并列以便于区别，请注意不同例子的特征长度相差可达1035。银河系的特征尺度量级为1022cm，而核子的尺度量级为10-13cm，用以说明逾渗理论广阔的适用范围。

评分☆☆☆☆☆

帮别人买得，还没来得及看，说是不错。

评分☆☆☆☆☆

帮别人买得，还没来得及看，说是不错。

评分☆☆☆☆☆

给别人买的，他说还行吧

评分☆☆☆☆☆

给别人买的，他说还行吧

评分☆☆☆☆☆

这类书并不多见，很值得看一看。所谓逾渗就是指在一元或多元体系中，体系以外的一种介质通过一定的路径进入体系内的过程。它是一种广泛存在的物理现象，既存在于微观世界，又存在于客观世界，如液体可以扩散及逾渗过程穿过无序的介质。

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给别人买的，他说还行吧

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