Positive harmonic functions for semi-isotropic random walks on trees, lamplighter groups, and DL-graphs (Q2502241)

The authors' results arise as a special case of a more general class of lamplighter type random walks, which arise as random walks on the Diestel-Leader graphs. For instance, a first result states the forms of every minimal \(P\)-harmonic functions. The methods, which are used in the paper, have their roots in the study of random walks on the affine group over the real.