Separation versus diffusion in a two species system

Abstract

We consider a finite number of particles that move in ZZ as independent random walks. The particles are of two species that we call aa and bb. The rightmost aa-particle becomes a bb-particle at constant rate, while the leftmost bb-particle becomes aa-particle at the same rate, independently. We prove that in the hydrodynamic limit the evolution is described by a nonlinear system of two PDE’s with free boundaries.