  We consider random walks on a non-elementary hyperbolic group endowed with a
word distance. To a probability measure on the group are associated two
numerical quantities, the rate of escape and the entropy. On the set of
admissible probability measures whose support is contained in a given finite
set, we show that both quantities depend in an analytic way on the probability
measure. Our spectral techniques also give a new proof of the central limit
theorem, and imply that the corresponding variance is analytic.
