Random Stirring of the Real Line

Abstract

Random stirring of the real line $R_1$ is defined. This notion is derived from a generalization of the nearest-neighbor simple exclusion model on the one-dimensional lattices discussed by Spitzer and by Harris. Under the random stirring, the motion of an infinite particle system is Markovian and has a Poisson process as an invariant probability measure. An ergodic theorem is established concerning the convergence of a system to a Poisson process.