Current fluctuations for stochastic particle systems with drift in one spatial dimension

Abstract

This review article discusses limit distributions and vari- ance bounds for particle current in several dynamical stochastic systems of particles on the one-dimensional integer lattice: independent particles, in- dependent particles in a random environment, the random average process, the asymmetric simple exclusion process, and a class of totally asymmetric zero range processes. The first three models possess linear macroscopic flux functions and lie in the Edwards-Wilkinson universality class with scaling exponent 1=4 for current fluctuations. For these we prove Gaussian limits for the current process. The latter two systems belong to the Kardar-Parisi- Zhang class. For these we prove the scaling exponent 1=3 in the form of upper and lower variance bounds.