Shock fluctuations for the Hammersley process

Abstract

We consider the Hammersley interacting particle system starting from a shock initial profile with densities (). The microscopic shock is taken as the position of a second-class particle initially at the origin, and the main results are: (i) a central limit theorem for the shock; (ii) the variance of the shock equals . By using the same method of proof, we also prove similar results for first-class particles.