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

Let X be a compact K & auml;hler manifold of complex dimension k >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\ge 2$$\end{document} and f:X -> X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f: X \rightarrow X$$\end{document} a holomorphic correspondence with simple action on cohomology such that f-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f<^>{-1}$$\end{document} 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.