  We study density of parabolic elements in a finitely generated relatively
hyperbolic group $G$ with respect to a word metric. We prove this density to be
zero (apart from degenerate cases) and the limit defining the density to
converge exponentially fast; this has recently been proven independently by W.
Yang. As a corollary, we obtain the analogous result for the set of commuting
pairs of elements in $G^2$, showing that the degree of commutativity of $G$ is
equal to zero.

Group Theory