Shock fluctuations for the Hammersley process

Abstract

We consider the Hammersley interacting particle system starting from a shock initial profile with densities $\lambda ,\rho \in \mathbb{R}$ ($\lambda >\rho$). The microscopic shock is taken as the position of a second-class particle initially at the origin, and the main results are: a central limit theorem for the shock; the variance of the shock equals $2[\lambda \rho (\lambda -\rho ){]}^{-1}t+O(t^{2/3})$. By using the same method of proof, we also prove similar results for first-class particles.

Hammersley process, multi-class particles, shock fluctuations. Final version, accepted for publication in the Journal of Statistical Physics

References in corpus (3)

• Stationary distributions of multi-type totally asymmetric exclusion processes
• Second class particles and cube root asymptotics for Hammersley's process
• Hammersley's process with sources and sinks