Positive harmonic functions for semi-isotropic random walks on trees, lamplighter groups, and DL-graphs

Details Positive harmonic functions for semi-isotropic random walks on trees, lamplighter groups, and DL-graphs Positive harmonic functions for semi-isotropic random walks on trees, lamplighter groups, and DL-graphs

2005-01-25

arxiv.org/abs/math/0501440v1

Mathematics

Probability

Scientific paper

We determine all positive harmonic functions for a large class of "semi-isotropic" random walks on the lamplighter group, i.e., the wreath product of the cyclic group of order q with the infinite cyclic group. This is possible via the geometric realization of a Cayley graph of that group as the Diestel-Leader graph DL(q,q). More generally, DL(q,r) is the horocyclic product of two homogeneous trees with respective degrees $q+1$ and $r+1$, and our result applies to all DL-graphs. This is based on a careful study of the minimal harmonic functions for semi-isotropic walks on trees.

Affiliated with

Also associated with

No associations

Rating

Positive harmonic functions for semi-isotropic random walks on trees, lamplighter groups, and DL-graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Positive harmonic functions for semi-isotropic random walks on trees, lamplighter groups, and DL-graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Positive harmonic functions for semi-isotropic random walks on trees, lamplighter groups, and DL-graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-513640