Exponential mixing of all orders on Kähler manifolds: (quasi-)plurisubharmonic observables
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916833672560640 |
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| author | Vergamini, Marco Wu, Hao |
| author_facet | Vergamini, Marco Wu, Hao |
| contents | 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 $μ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04183 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exponential mixing of all orders on Kähler manifolds: (quasi-)plurisubharmonic observables Vergamini, Marco Wu, Hao Complex Variables Dynamical Systems 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 $μ$. |
| title | Exponential mixing of all orders on Kähler manifolds: (quasi-)plurisubharmonic observables |
| topic | Complex Variables Dynamical Systems |
| url | https://arxiv.org/abs/2505.04183 |