Tagged particle fluctuations for TASEP with dynamics restricted by a moving wall

TL;DR

This paper analyzes the fluctuations of a tagged particle in a TASEP model with a moving wall, extending previous work by characterizing the distribution of the particle's position near multiple macroscopic times.

Contribution

It provides a detailed description of the limiting distribution of a tagged particle in TASEP with a moving wall at multiple macroscopic times, expanding prior results.

Findings

Derived the limiting distribution of the tagged particle near multiple macroscopic times.

Extended previous models to include the influence of a moving wall on particle fluctuations.

Provided new insights into the dynamics of TASEP with boundary restrictions.

Abstract

We consider the totally asymmetric simple exclusion process on $\Z$ with step initial condition and with the presence of a rightward-moving wall that prevents the particles from jumping. This model was first studied in [Borodin-Bufetov-Ferrari'21]. We extend their work by determining the limiting distribution of a tagged particle in the case where the wall has influence on its fluctuations in neighbourhoods of multiple macroscopic times.