Gerl, Peter

Rekurrente und transiente Bäme

Sémin. Lothar. Comb. 10, B10i, 8 p., electronic only (1984)


Summary: 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.