相互作用粒子系統 英文

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