《相互作用粒子系統(英文)》旨在為讀者全新展示隨機過程這門課程。在過去的十五年里這門課程有了更深入研究，文中的材料都是之前沒有以書本的形式出現過的。有關這門科技含量很高的科目，這本高質量的教程使得該科目立刻生動起來，並且儘可能多的包含一些容易理解的開放問題。對於每一位學習隨機課程的學生，此書都不容錯過。
基本介紹
- 書名：相互作用粒子系統
- 作者：里戈特 (Thomas M.Liggett)
- 出版社：世界圖書出版公司北京公司
- 頁數：496頁
- 開本：24
- 品牌：世界圖書出版公司北京公司
- 外文名：Interacting Particle Systems
- 類型：科學與自然
- 出版日期：2013年3月1日
- 語種：簡體中文, 英語
- ISBN：9787510058097
基本介紹,內容簡介,作者簡介,圖書目錄,
基本介紹
內容簡介
里戈特編著的《相互作用粒子系統》旨在為讀者全新展示隨機過程這門課程。在過去的十五年里這門課程有了更深入研究，文中的材料都是之前沒有以書本的形式出現過的。有關這門科技含量很高的科目，這本高質量的教程使得該科目立刻生動起來，並且儘可能多的包含一些容易理解的開放問題。對於每一位學習隨機課程的學生，本書都不容錯過。目次：結構和其他一般結果；一些基本工具；自旋系統；隨機Ising模型；投票模型；接觸法；最近粒子系統；排除過程；值在[0,∞ ]s上的線性系統。讀者對象：數學、金融、統計專業的本科生、研究生和相關的科研人員。
作者簡介
作者：（美國）里戈特（Thomas M.Liggett）
圖書目錄
Frequently Used Notation
Introduction
CHAPTER Ⅰ
The Construction, and Other General Results
1.Markov Processes and Their Semigroups
2.Semigroups and Their Generators
3.The Construction of Generators for Particle Systems
4.Applications of the Construction
5.The Martingale Problem
6.The Martingale Problem for Particle Systems
7.Examples
8.Notes and References
9.Open Problems
CHAPTER Ⅱ
Some Basic Tools
1.Coupling
2.Monotonicity and Positive Correlations
3.Duality
4.Relative Entropy
5.Reversibility
6.Recurrence and Transience of Reversible Markov Chains
7.Superpositions of Commuting Markov Chains
8.Perturbations of Random Walks
9.Notes and References
CHAPTER Ⅲ
Spin Systems
1.Couplings for Spin Systems
2.Attractive Spin Systems
3.Attractive Nearest-Neighbor Spin Systems on Z1
4.Duality for Spin Systems
5.Applications of Duality
6.Additive Spin Systems and the Graphical Representation
7.Notes and References
8.Open Problems
CHAPTER Ⅳ
Stochastic Ising Models
1.Gibbs States
2.Reversibility of Stochastic Ising Models
3.Phase Transition
4.L2 Theory
5.Characterization of Invariant Measures
6.Notes and References
7.Open Problems
CHAPTER Ⅴ
The Voter Model
1.Ergodic Theorems
2.Properties of the Invariant Measures
3.Clustering in One Dimension
4.The Finite System
5.Notes and References
CHAPTER Ⅵ
The Contact Process
1.The Critical Value
2.Convergence Theorems
3.Rates of Convergence
4.Higher Dimensions
5.Notes and References
6.Open Problems
CHAPTER Ⅶ
Nearest-Particle Systems
1.Reversible Finite Systems
2.General Finite Systems
3.Construction of Infinite Systems
4.Reversible Infinite Systems
5.General Infinite Systems
6.Notes and References
7.Open Problems
CHAPTER Ⅷ
The Exclusion Process
1.Ergodic Theorems for Symmetric Systems
2.Coupling and Invariant Measures for General Systems
3.Ergodic Theorems for Translation Invariant Systems
4.The Tagged Particle Process
5.Nonequilibrium Behavior
6.Notes and References
7.Open Problems
CHAPTER Ⅸ
Linear Systems with Values in [0, oo）s
1.The Construction; Coupling and Duality
2.Survival and Extinction
3.Survival via Second Moments
4.Extinction in One and Two Dimensions
5.Extinction in Higher Dimensions
6.Examples and Applications
7.Notes and References
8.Open Problems
Bibliography
Index
Postface
Errata
Introduction
CHAPTER Ⅰ
The Construction, and Other General Results
1.Markov Processes and Their Semigroups
2.Semigroups and Their Generators
3.The Construction of Generators for Particle Systems
4.Applications of the Construction
5.The Martingale Problem
6.The Martingale Problem for Particle Systems
7.Examples
8.Notes and References
9.Open Problems
CHAPTER Ⅱ
Some Basic Tools
1.Coupling
2.Monotonicity and Positive Correlations
3.Duality
4.Relative Entropy
5.Reversibility
6.Recurrence and Transience of Reversible Markov Chains
7.Superpositions of Commuting Markov Chains
8.Perturbations of Random Walks
9.Notes and References
CHAPTER Ⅲ
Spin Systems
1.Couplings for Spin Systems
2.Attractive Spin Systems
3.Attractive Nearest-Neighbor Spin Systems on Z1
4.Duality for Spin Systems
5.Applications of Duality
6.Additive Spin Systems and the Graphical Representation
7.Notes and References
8.Open Problems
CHAPTER Ⅳ
Stochastic Ising Models
1.Gibbs States
2.Reversibility of Stochastic Ising Models
3.Phase Transition
4.L2 Theory
5.Characterization of Invariant Measures
6.Notes and References
7.Open Problems
CHAPTER Ⅴ
The Voter Model
1.Ergodic Theorems
2.Properties of the Invariant Measures
3.Clustering in One Dimension
4.The Finite System
5.Notes and References
CHAPTER Ⅵ
The Contact Process
1.The Critical Value
2.Convergence Theorems
3.Rates of Convergence
4.Higher Dimensions
5.Notes and References
6.Open Problems
CHAPTER Ⅶ
Nearest-Particle Systems
1.Reversible Finite Systems
2.General Finite Systems
3.Construction of Infinite Systems
4.Reversible Infinite Systems
5.General Infinite Systems
6.Notes and References
7.Open Problems
CHAPTER Ⅷ
The Exclusion Process
1.Ergodic Theorems for Symmetric Systems
2.Coupling and Invariant Measures for General Systems
3.Ergodic Theorems for Translation Invariant Systems
4.The Tagged Particle Process
5.Nonequilibrium Behavior
6.Notes and References
7.Open Problems
CHAPTER Ⅸ
Linear Systems with Values in [0, oo）s
1.The Construction; Coupling and Duality
2.Survival and Extinction
3.Survival via Second Moments
4.Extinction in One and Two Dimensions
5.Extinction in Higher Dimensions
6.Examples and Applications
7.Notes and References
8.Open Problems
Bibliography
Index
Postface
Errata
