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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.

內頁插圖

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

前言/序言

逾滲（第2版）（英文版） [Percolation] 下載 mobi epub pdf txt 電子書

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逾滲理論是處理強無序和具有隨機幾何結構係統常用的理論方法之一。這一理論的研究中心內容是：當係統的成分或某種意義上的密度變化達到一定值（稱為逾滲閾值）時，在逾滲閾值處係統的一些物理性質會發生尖銳的變化，即在逾滲閾值處，係統的一些物理現象的連續性會消失（而從另一方麵看，則是突然齣現）。 逾滲轉變，指的是在龐大無序係統中隨著聯結程度，或某種密度、占據數、濃度的增加（或減少）到一定程度，係統內突然齣現（或消失）某種長程聯結性，性質發生突變，我們稱發生瞭逾滲轉變，或者說發生瞭尖銳的相變。正是這種逾滲轉變，使之成為描述多種不同現象的一個自然模型，用於闡明相變和臨界現象的一些最重要的物理概念，其中許多概念對非晶態固體（高分子材料是典型的一種）是十分有用的。逾滲理論的重要實際意義，在於它可廣泛應用於說明眾多物理、化學、生物及社會現象，迄今其應用範圍還在不斷擴大。錶5-1列舉瞭十五種不同的現象，都是已采用逾滲模型加以分析的。

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這類書並不多見，很值得看一看。所謂逾滲就是指在一元或多元體係中，體係以外的一種介質通過一定的路徑進入體係內的過程。它是一種廣泛存在的物理現象，既存在於微觀世界，又存在於客觀世界，如液體可以擴散及逾滲過程穿過無序的介質。

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不錯不錯不錯不錯不錯不錯不錯不錯不錯不錯不錯不錯不錯不錯不錯不錯

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錶1中約一半屬宏觀現象，一半屬微觀過程。宏觀和微觀的分界綫在錶的中間。這兒特意把兩種極端情形並列以便於區彆，請注意不同例子的特徵長度相差可達1035。銀河係的特徵尺度量級為1022cm，而核子的尺度量級為10-13cm，用以說明逾滲理論廣闊的適用範圍。

評分☆☆☆☆☆

錶1中約一半屬宏觀現象，一半屬微觀過程。宏觀和微觀的分界綫在錶的中間。這兒特意把兩種極端情形並列以便於區彆，請注意不同例子的特徵長度相差可達1035。銀河係的特徵尺度量級為1022cm，而核子的尺度量級為10-13cm，用以說明逾滲理論廣闊的適用範圍。

評分☆☆☆☆☆

評分☆☆☆☆☆

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