Harmonic functions on hyperbolic graphs

Petit, Camille

doi:10.1090/S0002-9939-2011-10931-6

Harmonic functions on hyperbolic graphs
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by Camille Petit PDF

Proc. Amer. Math. Soc. 140 (2012), 235-248 Request permission

Abstract:

We consider admissible random walks on hyperbolic graphs. For a given harmonic function on such a graph, we prove that asymptotic properties of non-tangential boundedness and non-tangential convergence are almost everywhere equivalent. The proof is inspired by the works of F. Mouton in the cases of Riemannian manifolds of pinched negative curvature and infinite trees. It involves geometric and probabilitistic methods.

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