Limit theorems for the position of a tagged particle in the stirring-exclusion process

摘要

Stirring-exclusion processes are exclusion processes with particles being stirred. We investigate a tagged particle among a Bernoulli product environment measure on the lattice Z~d. We show the strong law of large numbers and the central limit theorem for the tagged particle. The proof of the central limit theorem is based on the method of martingale decomposition with a sector condition.