Limit laws for biased random walks on a Galton-Watson tree with leaves
Résumé
We consider an outwardly $\beta$-biased random walk $X_n$ on a Galton-Watson tree with leaves in the sub-ballistic regime. We prove that $X_n/n^{\gamma}$ convergences in law and we characterize the limit law. The exponent $\gamma\in (0,1)$ is explicit and is a decreasing function of $\beta$. Key tools for the proof are classical decomposition results for Galton-Watson trees, a new variant of regeneration times and the careful analysis of the time the walker spends in leaves.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)