Hydrodynamic Limit for Exclusion Processes with Velocity

2011, v.17, №3, 391-428

ABSTRACT

We study a class of one-dimensional exclusion processes with velocities featuring random flips of the sign of velocities. We consider a system of particles with velocity +1 or -1 where particles interact with each other via hard-core exclusion potential. Each particle can only hop in the direction of its velocity. The sign of the velocity of each particle flips at rate $\gamma > 0$. We prove the hydrodynamic limit for this nonreversible and nongradient system under the diffusive space-time scaling. The hydrodynamic equation is a certain nonlinear diffusion equation and its diffusion coefficient is characterized by a variational formula. We also obtain the asymptotic behavior of the diffusion coefficient as $\gamma$ goes to $\infty$ or $0$.

Keywords: hydrodynamic limit,interacting particle systems,exclusion processes