Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An approach to traces of random walks on the boundary of a hyperbolic
  group via reflected Dirichlet spaces   On a non elementary, Gromov hyperbolic group of conformal dimension less than
two - say a surface group - we consider a symmetric probability measure whose
support generates the whole group and with a finite second moment. To such a
probability measure, we associate a Besov space on the boundary of the group.
All the Besov spaces constructed that way turn out to be isomorphic. They are
also isomorphic to the Besov spaces already constructed by M. Bourdon and H.
Pajot using the cohomology of the group. In our work, cohomology spaces are
replaced by martingales. We also provide a probabilistic interpretation of the
Besov spaces as the Dirichlet spaces of the trace on the boundary of the random
walks reflected on the boundary. Along with the definition of Besov spaces,
come notions of sets of zero capacity, smooth measures and measures of finite
energy on the boundary. Using heat kernel estimates, we obtain an integral
criterion for a measure on the boundary to have finite energy. We apply this
criterion and deviation inequalities to show that harmonic measures of random
walks with a driving measure with a finite first moment are smooth measures in
our sense, thus obtaining a quite general regularity property of harmonic
measures.

33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph