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Séminaire Lotharingien de Combinatoire, B10h (1984).

[Formerly: Publ. I.R.M.A. Strasbourg, 1987, 340/S-10, p.
80-87.]

# Peter Gerl

# Rekurrente und transiente Bäme

**Abstract.**
A connected graph is called *transient* if with probability greater
than 0 a random walk starting from some vertex does not return to this
vertex, otherwise it is called *recurrent*. We ask the question of
what can be said about trees in **Z**^{3}: which trees are
recurrent, which trees which are transient? We discuss several
examples in which we determine whether they are recurrent or transient.
Moreover, we conjecture that trees which "grow slowly" (in a precise
sense) are recurrent.
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