Equilibrium Fluctuations for the Totally Asymmetric Zero Range process

TL;DR

This paper proves a CLT for the empirical measure in the 1D Totally Asymmetric Zero-Range Process at equilibrium, revealing non-evolving fluctuation fields and vanishing currents over extended time scales.

Contribution

It establishes a CLT for the process and uncovers the non-evolution of fluctuation fields along characteristics in a longer time scale.

Findings

Proves a CLT for the empirical measure in the process.

Shows fluctuation fields do not evolve in time along characteristics.

Demonstrates the current across characteristics vanishes in longer time scales.

Abstract

We prove a Central Limit Theorem for the empirical measure in the one-dimensional Totally Asymmetric Zero-Range Process in the hyperbolic scaling $N$, starting from the equilibrium measure $\nu_{\rho}$. We also show that when taking the direction of the characteristics, the limit density fluctuation field does not evolve in time until $N^{4/3}$, which implies the current across the characteristics to vanish in this longer time scale.