  Let $f$ be a complex H\'enon map and $\mu$ its unique measure of maximal
entropy. We prove that $\mu$ is exponentially mixing of all orders for all (not
necessarily bounded) plurisubharmonic observables, and that all
plurisubharmonic functions satisfy the central limit theorem with respect to
$\mu$. Our results hold more generally for every H\'enon-Sibony map on
$\mathbb{C}^k$.
