The speed of the tagged particle in the exclusion process on galton–watson trees

We study two different versions of the simple exclusion process on augmented Galton– Watson trees, the constant speed model and the variable 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.