Abstract Let f be a holomorphic automorphism of a compact Kähler manifold with simple action on cohomology and μ its unique measure of maximal entropy. We prove that μ is exponentially mixing of all orders for all d. s. h. observables, i. e. , functions that are locally differences of plurisubharmonic functions. As a consequence, every d. s. h. observable satisfies the central limit theorem with respect to μ.
Vergamini et al. (Thu,) studied this question.