On Random Walks on Polynomial Trees

In this thesis we study the long-term behaviour of different random processes on polynomial trees. The questions we answer concern whether the process will return to its initial location infinitely often or not. We answer these questions by relating key parameters in the processes we study to the geometry of the tree on which the processes are defined. We study processes whose probabilities to move from one vertex to another are themselves random variables, and processes where these probabilities are reinforced, or updated.