| | | | 逾滲-第2版 科學與自然 Geoffrey Grimmett[著] 世界圖書出版公司 | | 該商品所屬分類：圖書 -> ε | | 【市場價】 | 608-880元 | | 【優惠價】 | 380-550元 | | 【出版社】 | 世界圖書出版公司北京公司 | | 【ISBN】 | 9787510046292 | | 【折扣說明】 | 一次購物滿999元台幣免運費+贈品
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| | 內容介紹 | |
出版社：世界圖書出版公司北京公司 ISBN：9787510046292 商品編碼：70983142772 開本：大32開 出版時間：2012-08-01 頁數：444 代碼：69
"| 商品基本信息，請以下列介紹為準 | | 商品名稱： | 逾滲-第2版 | | 作者： | Geoffrey Grimmett[著] | | 代碼： | 69.0 | | 出版社： | 圖書出版公司北京公司 | | 出版日期： | 2012-08-01 | | ISBN： | 9787510046292 | | 印次： | 1 | | 版次： | 1 | | 裝幀： | | | 開本： | 大32開 |
| 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 |
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