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1. INTRODUCTION. The delight of finding unexpected connections is one of the rewards of studying mathematics. In this paper we present connections that link the following seven superficially unrelated entities:

We study the potential theory of trees with nearest-neighbor transition probability that yields a recurrent random walk and show that, although such trees have no positive potentials, many of the standard results of potential theory can be transferred to this setting. We accomplish this by defining a non-negative function H, harmonic outside the root e and… (More)

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