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Considering a random walk on an infinite tree, we suppose that transition probabilities are "reasonnable", id est that they are bounded between two constants taken in (0, 1/2). It is shown that, for a given harmonic function on the tree, properties of radial convergence, radial boundedness, finiteness of radial energy and corresponding stochastic notions are all equivalent at almost each point of the geometric boundary. The idea of the proof comes from an analoguous result on Riemannian manifolds of pinched negative curvature due to the author.

Comportement asymptotique des fonctions harmoniques sur les arbres