On the Cover time of $λ$-biased walk on supercritical Galton-Watson trees

Tianyi Bai

Published 2019-05-14Version 1

In this paper we study the time required for a $\lambda$-biased ($\lambda>1$) walk to visit all nodes of a supercritical Galton-Watson tree up to generation $n$. Inspired by the extremal landscape approach in [Cortines et al. 2018] for simple random walk on binary trees, we establish the near-independent nature of extremal points for the $\lambda$-biased walk, and deduce the scaling limit of the cover time.