Boundary theory on the Hata tree

We prove that for a certain Markov chain on the symbolic space of the Hata tree KK, the Martin boundary MM is homeomorphic to the trunk   of the Hata tree, and the minimal Martin boundary is the post-critical set {12̇,1̇,2̇}, which corresponds to the three vertices of the trunk. Moreover, the class of PP-harmonic functions on MM coincides with Kigami’s class of harmonic functions on KK.