preprint
Inserted: 9 mar 2026
Last Updated: 9 mar 2026
Year: 2025
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 $μ$.