# On the cover time of {\lambda}-biased walk on supercritical Galton-Watson trees

## TL;DR

This paper investigates the cover time of a biased walk on supercritical Galton-Watson trees, establishing its scaling limit and extending extremal landscape methods from simple random walks to biased cases.

## Contribution

It introduces the first analysis of cover times for {}-biased walks on supercritical Galton-Watson trees, extending extremal landscape techniques to biased settings.

## Key findings

- Derived the scaling limit of cover time for biased walks.
- Extended extremal landscape approach to biased random walks.
- Provided new insights into traversal times on complex trees.

## Abstract

In this paper, we study the time required for a {\lambda}-biased ({\lambda}>1) walk to visit all the vertices of a supercritical Galton-Watson tree up to generation n. Inspired by the extremal landscape approach in [Cortines, Louidor, Saglietti 2018] for the simple random walk on binary trees, we establish the scaling limit of the cover time in the biased setting.