Equilibrium fluctuations for totally asymmetric interacting particle systems

Abstract

We study equilibrium fluctuations for a class of totally asymmetric zero-range type interacting particle systems. As a main result, we show that density fluctuation of our process converges to the stationary energy solution of the stochastic Burgers equation. As a special case, microscopic system we consider here is related to q-totally asymmetric simple exclusion processes (q-TASEPs) and our scaling limit corresponds to letting the quantum parameter q to be one.