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

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

2010-04-26

arxiv.org/abs/1004.4416v1

Mathematics

Metric Geometry

7 pages

Scientific paper

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.

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