# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1903.05019