The Construction, and Other General Results
The interacting particle systems which are the subject of this book are continuous-time Markov processes on certain spaces of configurations of particles. These processes are normally specified by giving the infinitesimal rates at which transitions occur. In general there are infinitely many particles in the system, and infinitely many of them make transitions in any interval of time. The transition rates for individual particles can depend on the entire configuration. Consequently, it is not immediately clear whether the specification of the local dynamics determines the evolution of the system as a whole in a unique way. Before proceeding to analyze the infinite system, it is therefore necessary to examine this question of existence and uniqueness of the process.
KeywordsMarkov Process Invariant Measure Transition Rate Particle System Exclusion Process
Unable to display preview. Download preview PDF.