Non-tangential, radial and stochastic asymptotic properties of harmonic functions on trees

Frédéric Mouton (1)

1 IF - Institut Fourier

For a harmonic function on a tree with random walk whose transition probabilities are bounded between two constants in (0,1/2), it is known that the radial and stochastic properties of convergence, boundedness and finiteness of energy are all a.s. equivalent. We prove here that the analogous non-tangential properties are a.e. equivalent to the above ones.

Mots clés: harmonic functions; trees; Fatou theorem; random walks

Domaines: Géométrie métrique [math.MG]; Probabilités [math.PR]

Frédéric Mouton. Non-tangential, radial and stochastic asymptotic properties of harmonic functions on trees. 2009. ⟨hal-00475206⟩