Microscopic structure of a decreasing shock for the asymmetric $k$-step exclusion process

Abstract

The asymmetric $k$-step exclusion processes are the simplest interacting particle systems whose hydrodynamic equation may exhibit both increasing and decreasing entropic shocks under Euler scaling. We prove that, under Riemann initial condition with right density zero and adequate left density, the rightmost particle identifies microscopically the decreasing shock.