Exponential mixing of all orders and CLT for automorphisms of compact K{\"a}hler manifolds

Fabrizio Bianchi; Tien-Cuong Dinh

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arXiv · 2304.13335

Exponential mixing of all orders and CLT for automorphisms of compact K{\"a}hler manifolds

Fabrizio Bianchi·Tien-Cuong Dinh

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Abstract

We consider the unique measure of maximal entropy of an automorphism of a compact K{\"a}hler manifold with simple action on cohomology. We show that it is exponentially mixing of all orders with respect to H{\"o}lder observables. It follows that the Central Limit Theorem (CLT) holds for these observables. In particular, our result applies to all automorphisms of compact K{\"a}hler surfaces with positive entropy.

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Fabrizio Bianchi, Tien-Cuong Dinh. 2023-04-26. Exponential mixing of all orders and CLT for automorphisms of compact K{\"a}hler manifolds. https://arxiv.org/abs/2304.13335

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