Linear drift and Poisson boundary for random walks
2007 (English)In: Pure and Applied Mathematics Quarterly, ISSN 1558-8599, Vol. 3, no 4, 1027-1036 p.Article in journal (Refereed) Published
We consider a nondegenerate random walk on a locally compact group with finite first moment. Then, if there are no nonconstant bounded harmonic functions, all the linear drift comes from a real additive character on the group. As a corollary we obtain a generalization of Varopoulos' theorem that in the case of symmetric random walks, positive linear drift implies the existence of nonconstant bounded harmonic functions. Another consequence is the phenomenon that for some groups (including certain Grigorchuk groups) the drift vanishes for any measure of finite first moment.
Place, publisher, year, edition, pages
2007. Vol. 3, no 4, 1027-1036 p.
markov-chains, entropy, growth
IdentifiersURN: urn:nbn:se:kth:diva-17234ISI: 000254784000008ScopusID: 2-s2.0-42949153861OAI: oai:DiVA.org:kth-17234DiVA: diva2:335277
QC 201005252010-08-052010-08-05Bibliographically approved