  We prove a generalization of the fundamental inequality of Guivarc'h relating
entropy, drift and critical exponent to Gibbs measures on geometrically finite
quotients of CAT(-1) metric spaces. For random walks with finite
superexponential moment, we show that the equality is achieved if and only if
the Gibbs density is equivalent to the hitting measure. As a corollary, if the
action is not convex cocompact, any hitting measure is singular to any Gibbs
density.
