Author | Liggett, Thomas M. author |
---|---|
Title | Interacting Particle Systems [electronic resource] / by Thomas M. Liggett |
Imprint | New York, NY : Springer New York, 1985 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-8542-4 |
Descript | XIII, 488 p. online resource |
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 -- 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 -- 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 -- 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 -- 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 -- 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 -- 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 -- 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