by Mu-Fa Chen (Beijing Normal University, China)

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. It also deals with a typical class of non-equilibrium particle systems, including the typical Schlögl model taken from statistical physics. The constructions, ergodicity and phase transitions for this class of Markov interacting particle systems, namely, reaction–diffusion processes, are presented. In this new edition, a large part of the text has been updated and two-and-a-half chapters have been rewritten. The book is self-contained and can be used in a course on stochastic processes for graduate students.

• An Overview of the Book: Starting from Markov Chains
• General Jump Processes:
  • Transition Function and Its Laplace Transform
  • Existence and Simple Constructions of Jump Processes
  • Uniqueness Criteria
  • Recurrence, Ergodicity and Invariant Measures
  • Probability Metrics and Coupling Methods
• Symmetrizable Jump Processes:
  • Symmetrizable Jump Processes and Dirichlet Forms
  • Field Theory
  • Large Deviations
  • Spectral Gap
• Equilibrium Particle Systems:
  • Random Fields
  • Reversible Spin Processes and Exclusion Processes
  • Yang–Mills Lattice Field
• Non-Equilibrium Particle Systems:
  • Constructions of the Processes
  • Existence of Stationary Distributions and Ergodicity
  • Phase Transitions
  • Hydrodynamic Limits