Equidistribution of graphs of holomorphic correspondences

Let X be a compact Riemann surface. Let f be a holomorphic self-correspondence of X with dynamical degrees d₁ and d₂. Assume that d₁≠ d₂ or f is non-weakly modular. We show that the graphs of the iterates fⁿ of f are equidistributed exponentially fast with respect to a positive closed current in X× X.