A note on the Martin boundary of the simple random walk on an example of directed graph

Details A note on the Martin boundary of the simple random walk on an example of directed graph A note on the Martin boundary of the simple random walk on an example of directed graph

2012-03-15

arxiv.org/abs/1203.3314v1

Mathematics

Probability

Scientific paper

In this note, we study the Martin boundary of the simple random walk on an
example of directed graph. More precisely, the Martin boundary is shown to be
trivial, i.e. there is no non-constant positive harmonic functions. The proof
involves fine estimates of the Green function which are summarized in this
note.

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