Displaying similar documents to “The Martin Boundary for Harmonic Functions on Groups of Automorphisms of a Homogeneous Tree.”

Asymptotic properties of harmonic measures on homogeneous trees

Konrad Kolesko (2010)

Colloquium Mathematicae

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Let Aff(𝕋) be the group of isometries of a homogeneous tree 𝕋 fixing an end of its boundary. Given a probability measure on Aff(𝕋) we consider an associated random process on the tree. It is known that under suitable hypothesis this random process converges to the boundary of the tree defining a harmonic measure there. In this paper we study the asymptotic behaviour of this measure.

Local admissible convergence of harmonic functions on non-homogeneous trees

Massimo A. Picardello (2010)

Colloquium Mathematicae

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We prove admissible convergence to the boundary of functions that are harmonic on a subset of a non-homogeneous tree equipped with a transition operator that satisfies uniform bounds suitable for transience. The approach is based on a discrete Green formula, suitable estimates for the Green and Poisson kernel and an analogue of the Lusin area function.