Positive Harmonic Functions for Semi-isotropic Random Walks on Trees, Lamplighter Groups, and Dl-graphs

@inproceedings{Woess2005PositiveHF,
  title={Positive Harmonic Functions for Semi-isotropic Random Walks on Trees, Lamplighter Groups, and Dl-graphs},
  author={Wolfgang Woess},
  year={2005}
}
We determine all positive harmonic functions for a large class of " semi-isotropic " random walks on the lamplighter group, i.e., the wreath product Z q ≀ Z, where q ≥ 2. 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) (q, r ≥ 2) 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… CONTINUE READING

From This Paper

Figures, tables, and topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 20 references

Rate of escape of random walks

FoS P FoSP Algorithmen
2007

Isoperimetry for wreath products of Markov chains and multiplicity of selfintersections of random walks , preprint

A. G. Erschler
2004

Renewal theory on the affine group of an oriented tree

S. Brofferio
J . Theoret . Probab . • 2004

The spectral measure of certain elements of the complex group ring of a wreath product

W. Dicks, Th. Schick
Geom . Dedicata • 2002

On the asymptotics of the rate of departure to infinity ( Russian )

A. G. Erschler
Zap . Nauchn . Sem . S .Peterburg . Otdel . Mat . Inst . Steklov . ( POMI ) • 2001

Random walks on DiestelLeader graphs , Abh

D. Bertacchi
Math . Sem . Univ . Hamburg • 2001

The lamplighter group as a group generated by a 2 - state automaton , and its spectrum

R. I. Grigorchuk, A. Żuk
Geom . Dedicata • 2001

Similar Papers

Loading similar papers…