In this paper we study the time required for a @math -biased ( @math ) walk to visit all nodes of a supercritical Galton-Watson tree up to generation @math . Inspired by the extremal landscape approach in [ 2018] for simple random walk on binary trees, we establish the near-independent nature of extremal points for the @math -biased walk, and deduce the scaling limit of the cover time.
Bounds using hitting time were given in Matthews @cite_17 , @math where @math is the expected time for the walk starting at @math to hit @math .
@cite_17
2068008593
On donne des bornes superieures et inferieures sur la fonction generatrice des moments du temps pris par une chaine de Markov pour visiter au moins n des N sous-ensembles selectionnes de son espace d'etats