Nonequilibrium fluctuations for a tagged particle in one-dimensional sublinear rate zero-range processes

TL;DR

This paper investigates the non-equilibrium fluctuations of a tagged particle in one-dimensional zero-range processes with sublinear rates, introducing a new approach to handle their unique mixing properties and extending results to second-class particles.

Contribution

It develops a novel method for establishing local replacement limits in sublinear rate zero-range processes, expanding understanding beyond linear rate models.

Findings

Derived non-equilibrium fluctuation results for tagged particles

Established a new approach for local replacement limits in sublinear systems

Captured fluctuations of second-class particles in symmetric models

Abstract

Nonequilibrium fluctuations of a tagged, or distinguished particle in a class of one dimensional mean-zero zero-range systems with sublinear, increasing rates are derived. In Jara-Landim-Sethuraman (2009), processes with at least linear rates are considered. A different approach to establish a main "local replacement" limit is required for sublinear rate systems, given that their mixing properties are much different. The method discussed also allows to capture the fluctuations of a "second-class" particle in unit rate, symmetric zero-range models.