Scaling limits of a tagged particle in the exclusion process with variable diffusion coefficient

TL;DR

This paper establishes the large-scale behavior of a tagged particle in a one-dimensional exclusion process with variable diffusion, showing convergence to fractional Brownian motion with Hurst 1/4.

Contribution

It introduces new scaling limits for a tagged particle in exclusion processes with variable diffusion coefficients, including a CLT with fractional Brownian motion.

Findings

Law of large numbers for the tagged particle

Central limit theorem with fractional Brownian motion (Hurst 1/4)

Scaling limits derived from zero-range process with bond disorder

Abstract

We prove a law of large numbers and a central limit theorem for a tagged particle in a symmetric simple exclusion process in the one-dimensional lattice with variable diffusion coefficient. The scaling limits are obtained from a similar result for the current through -1/2 for a zero-range process with bond disorder. For the CLT, we prove convergence to a fractional Brownian motion of Hurst exponent 1/4.