Exponential mixing of all orders on K\"ahler manifolds: (quasi-)plurisubharmonic observables

Abstract

Let $f$ be a holomorphic automorphism of a compact K\"ahler manifold with simple action on cohomology and $\mu$ its unique measure of maximal entropy. We prove that $\mu$ 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 $\mu$.