From Markov Chains to Non-equilibrium Particle Systems -- Contents -- Preface to the First Edition -- Preface to the Second Edition -- Chapter 0. An Overview of the Book: Starting from Markov Chains -- 0.1. Three Classical Problems for Markov Chains -- 0.2. Probability Metrics and Coupling Methods -- 0.3. Reversible Markov Chains -- 0.4. Large Deviations and Spectral Gap -- 0.5. Equilibrium Particle Systems -- 0.6. Non-equilibrium Particle Systems -- Part I. General Jump Processes -- Chapter 1. Transition Function and its Laplace Transform -- 1.1. Basic Properties of Transition Function -- 1.2. The q-Pair -- 1.3. Differentiability -- 1.4. Laplace Transforms -- 1.5. Appendix -- 1.6. Notes -- Chapter 2. Existence and Simple Construction of Jump Processes -- 2.1. Minimal Nonnegative Solutions -- 2.2. Kolmogorov Equations and Minimal Jump Process -- 2.3. Some Sufficient Conditions for Uniqueness -- 2.4. Kolmogorov Equations and q-Condition -- 2.5. Entrance Space and Exit Space -- 2.6. Construction of q-Processes with Single-Exit q-Pair -- 2.7. Notes -- Chapter 3. Uniqueness Criteria -- 3.1. Uniqueness Criteria Based on Kolmogorov Equations -- 3.2. Uniqueness Criterion and Applications -- 3.3. Some Lemmas -- 3.4. Proof of Uniqueness Criterion -- 3.5. Notes -- Chapter 4. Recurrence, Ergodicity and Invariant Measures -- 4.1. Weak Convergence -- 4.2. General Results -- 4.3. Markov Chains: Time-discrete Case -- 4.4. Markov Chains: Time-continuous Case -- 4.5. Single Birth Processes -- 4.6. Invariant Measures -- 4.7. Notes -- Chapter 5. Probability Metrics and Coupling Methods -- 5.1. Minimum Lp-Metric -- 5.2. Marginality and Regularity -- 5.3. Successful Coupling and Ergodicity -- 5.4. Optimal Markovian Couplings -- 5.5. Monotonicity -- 5.6. Examples -- 5.7. Notes -- Part II. Symmetrizable Jump Processes.

Chapter 6. Symmetrizable Jump Processes and Dirichlet Forms -- 6.1. Reversible Markov Processes -- 6.2. Existence -- 6.3. Equivalence of Backward and Forward Kolmogorov Equations -- 6.4. General Representation of Jump Processes -- 6.5. Existence of Honest Reversible Jump Processes -- 6.6. Uniqueness Criteria -- 6.7. Basic Dirichlet Form -- 6.8. Regularity, Extension and Uniqueness -- 6.9. Notes -- Chapter 7. Field Theory -- 7.1. Field Theory -- 7.2. Lattice Field -- 7.3. Electric Field -- 7.4. Transience of Symmetrizable Markov Chains -- 7.5. Random Walk on Lattice Fractals -- 7.6. A Comparison Theorem -- 7.7. Notes -- Chapter 8. Large Deviations -- 8.1. Introduction to Large Deviations -- 8.2. Rate Function -- 8.3. Upper Estimates -- 8.4. Notes -- Chapter 9. Spectral Gap -- 9.1. General Case: an Equivalence -- 9.2. Coupling and Distance Method -- 9.3. Birth-Death Processes -- 9.4. Splitting Procedure and Existence Criterion -- 9.5. Cheeger's Approach and Isoperimetric Constants -- 9.6. Notes -- Part III. Equilibrium Particle Systems -- Chapter 10. Random Fields -- 10.1. Introduction -- 10.2. Existence -- 10.3. Uniqueness -- 10.4. Phase Transition: Peierls Method -- 10.5. Ising Model on Lattice Fractals -- 10.6. Reflection Positivity and Phase Transitions -- 10.7. Proof of the Chess-Board Estimates -- 10.8. Notes -- Chapter 11. Reversible Spin Processes and Exclusion Processes -- 11.1. Potentiality for Some Speed Functions -- 11.2. Constructions of Gibbs States -- 11.3. Criteria for Reversibility -- 11.4. Notes -- Chapter 12. Yang-Mills Lattice Field -- 12.1. Background -- 12.2. Spin Processes from Yang-Mills Lattice Fields -- 12.3. Diffusion Processes from Yang-Mills Lattice Fields -- 12.4. Notes -- Part IV. Non-equilibrium Particle Systems -- Chapter 13. Constructions of the Processes -- 13.1. Existence Theorems for the Processes.

13.2. Existence Theorem for Reaction-Diffusion Processes -- 13.3. Uniqueness Theorems for the Processes -- 13.4. Examples -- 13.5. Appendix -- 13.6. Notes -- Chapter 14. Existence of Stationary Distributions and Ergodicity -- 14.1. General Results -- 14.2. Ergodicity for Polynomial Model -- 14.3. Reversible Reaction-Diffusion Processes -- 14.4. Notes -- Chapter 15. Phase Transitions -- 15.1. Duality -- 15.2. Linear Growth Model -- 15.3. Reaction-Diffusion Processes with Absorbing State -- 15.4. Mean Field Method -- 15.5. Notes -- Chapter 16. Hydrodynamic Limits -- 16.1. Introduction: Main Results -- 16.2. Preliminaries -- 16.3. Proof of Theorem 16.1 -- 16.4. Proof of Theorem 16.3 -- 16.5. Notes -- Bibliography -- Author Index -- Subject Index.