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