Application of entropy analysis to discrete-time interacting particle systems on the one-dimensional lattice. (English) Zbl 0951.60098

Yaguchi, Hirotake

Hiroshima Math. J. 30, No. 1, 137-165 (2000).

Summary: Stationary measures for discrete-time interacting particle systems on the one-dimensional lattice are considered. In our systems infinitely many particles can change their states simultaneously, and the change of each particle state is affected by particles on the surrounding sites. We extensively improve the relative entropy method and make it applicable to such discrete-time particle systems generally. We prove that the stationary measures for Ising models are given by a unique Gibbs state and those for exclusion processes are given by canonical Gibbs states.

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
60J05	Discrete-time Markov processes on general state spaces

Keywords:

interacting particle system; stochastic Ising model; exclusion process; relative entropy; Markov process; stationary measure; discrete time