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We show the existence of a trace process at infinity for random walks onhyperbolic groups of conformal dimension < 2 and relate it to the existence ofa reflecting random walk. To do so, we employ the theory of Dirichlet formswhich connects the theory of symmetric Markov processes to functional analyticperspectives. We introduce a family of Besov spaces associated to random walksand prove that they are isomorphic to some of the Besov spaces constructed fromthe co-homology of the group studied in Bourdon-Pajot (2003). We also study theregularity of harmonic measures of random walks on hyperbolic groups using thepotential theory associated to Dirichlet forms.

Besov spaces and random walks on a hyperbolic group: boundary traces and reflecting extensions of Dirichlet forms