The speed of the tagged particle in the exclusion process on Galton-Watson trees

TL;DR

This paper investigates the movement speed of a tagged particle in exclusion processes on Galton-Watson trees, providing explicit formulas and demonstrating positive linear speed in both constant and varying speed models.

Contribution

It introduces and analyzes two versions of exclusion processes on Galton-Watson trees, deriving explicit formulas for the tagged particle speeds.

Findings

Tagged particle has positive linear speed in both models

Explicit formulas for particle speeds are provided

Results hold for initial equilibrium distributions with non-zero density

Abstract

We study two different versions of the simple exclusion process on augmented Galton-Watson trees, the constant speed model and the varying speed model. In both cases, the simple exclusion process starts from an equilibrium distribution with non-vanishing particle density. Moreover, we assume to have initially a particle in the root, the tagged particle. We show for both models that the tagged particle has a positive linear speed and we give explicit formulas for the speeds.