We determine the Martin boundary for aperiodic simple random walk on a bi-tree, 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.
Publié le : 1994-10-14
Classification:
Martin boundary,
positive harmonic functions,
Green kernel,
Martin kernel,
renewal theorem,
60J50,
60J15,
05C05
@article{1176988500,
author = {Picardello, Massimo A. and Woess, Wolfgang},
title = {The Full Martin Boundary of the Bi-Tree},
journal = {Ann. Probab.},
volume = {22},
number = {4},
year = {1994},
pages = { 2203-2222},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988500}
}
Picardello, Massimo A.; Woess, Wolfgang. The Full Martin Boundary of the Bi-Tree. Ann. Probab., Tome 22 (1994) no. 4, pp. 2203-2222. http://gdmltest.u-ga.fr/item/1176988500/