Shock fluctuations for the Hammersley process
We consider the Hammersley interacting particle system starting from a shock initial profile with densities $λ,ρ\in\mathbb{R}$ ($λ> ρ$). 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 $2[λρ(λ- ρ)]^{-1}t + O(t^{2/3})$. By using the same method of proof, we also prove similar results for first-class particles.
math.PR↗