Equidistribution for non-pluripolar currents with respect to holomorphic correspondences of compact Kähler manifolds

Let X be a compact Kähler manifold of complex dimension \(k\ge 2\) $k\ge 2$ and \(f: X \rightarrow X\) $f:X\to X$ a holomorphic correspondence with simple action on cohomology such that \(f^{-1}\) $f^{-1}$ is also a holomorphic correspondence. We prove that the sequence of normalized pull-backs of a non-pluripolar current under iterates of f converges to the Green current associated with f.