The full Martin boundary of the bi-tree. (English) Zbl 0840.60073

Picardello, Massimo A.; Woess, Wolfgang

Ann. Probab. 22, No. 4, 2203-2222 (1994).

From the authors’ summary: We determine the Martin boundary for aperiodic simple random walk on a bitree, that is, the Cartesian product of two homogeneous trees. This is obtained by first deriving a “renewal theorem”, giving an asymptotic estimate of the Green kernel as the space variable tends to infinity. The basic tool is a result of Lalley that gives a uniform estimate of transition probabilities of nearest neighbour random walks on trees.

Reviewer: V.Lotov (Novosibirsk)

MSC:

60J50	Boundary theory for Markov processes
60G50	Sums of independent random variables; random walks
05C05	Trees

Keywords:

Martin boundary; positive harmonic functions; Green kernel; Martin kernel; renewal theorem