Abstract
In this paper, we study a connected non-parabolic, or transient, network compactified with the Kuramochi boundary, and show that the rand om walk converges almost surely to a random variable valued in the harmonic boundary, and a function of finite Dirichlet energy converges along the random walk to a random variable almost surely and in L 2 . We also give integral representations of solutions of Pois son equations on the Kuramochi compactification.
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