Convex projective surfaces, a generalization of hyperbolic surfaces, are naturally equipped with a geometric length function: the Hilbert length. We study the dynamics of the Hilbert length renormalized by its topological entropy, i.e. the exponential growth rate of closed geodesics. We estimate the number of closed geodesics which have roughly the same renormalized Hilbert length for two different convex projective surfaces. Furthermore, we study the resulting correlation number along special sequences of convex projective surfaces. This is joint work with Xian Dai. Speaker(s): Giuseppe Martone (University of Michigan)