680 research outputs found
Green kernel estimates and the full Martin boundary for random walks on lamplighter groups and Diestel-Leader graphs
We determine the precise asymptotic behaviour (in space) of the Green kernel
of simple random walk with drift on the Diestel-Leader graph , where
. The latter is the horocyclic product of two homogeneous trees with
respective degrees and . When , it is the Cayley graph of the
wreath product (lamplighter group) with respect
to a natural set of generators. We describe the full Martin compactification of
these random walks on -graphs and, in particular, lamplighter groups. This
completes and provides a better approach to previous results of Woess, who has
determined all minimal positive harmonic functions.Comment: 26 page
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