Some problems in potential theory on the polytrees

Moving a continuous problem to a discrete setting is a popular and everpresent approach, that (from time to time) allows to single out the geometric and combinatorial issues of the question ad hand. A particular case we are aiming to investigate is the representation of the unit disc (polydisc) by a dyadic tree (cartesian product of dyadic trees), and its connection to Dirichlet type spaces. Following Arcozzi, Rochberg, Sawyer and Wick we give a (very brief) introduction to the potential theory on a polytree, and then present a very incomplete list of related problems.