Equilibrium fluctuations for totally asymmetric interacting particle systems

TL;DR

This paper investigates the equilibrium fluctuations of a class of totally asymmetric zero-range particle systems, demonstrating their convergence to solutions of the stochastic Burgers equation, with connections to q-TASEP models.

Contribution

It establishes the convergence of density fluctuations in zero-range systems to the stochastic Burgers equation, linking microscopic models to macroscopic stochastic PDEs.

Findings

Density fluctuations converge to the stationary energy solution of the stochastic Burgers equation.

Special case relates the microscopic system to q-TASEP models as q approaches one.

Provides a rigorous scaling limit connecting particle systems to stochastic PDEs.

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.