An overview of the book : starting from Markov chains -- pt. I. General jump processes -- Ch. 1. Transition function and its Laplace transform -- Ch. 2. Existence and simple constructions of jump processes -- Ch. 3. Uniqueness criteria -- Ch. 4. Recurrence, ergodicity and invariant measures -- Ch. 5. Probability metrics and coupling methods -- pt. II. Symmetrizable jump processes -- Ch. 6. Symmetrizable jump processes and Dirichlet forms -- Ch. 7. Field theory -- Ch. 8. Large deviations -- Ch. 9. Spectral gap -- pt. III. Equilibrium particle systems -- Ch. 10. Random fields -- Ch. 11. Reversible spin processes and exclusion processes -- Ch. 12. Yang-Mills lattice field -- pt. IV. Non-equilibrium particle systems -- Ch. 13. Constructions of the processes -- Ch. 14. Existence of stationary distributions and ergodicity -- Ch. 15. Phase transitions -- Ch. 16. Hydrodynamic limits
Summary
This book is representative of the work of Chinese probabilists on probability theory and its applications in physics. It presents a unique treatment of general Markov jump processes: uniqueness, various types of ergodicity, Markovian couplings, reversibility, spectral gap, etc
Bibliography
Includes bibliographical references (pages 572-588) and indexes
