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<p>Let <i>f</i> be a holomorphic automorphism of a compact Kähler manifold with simple action on cohomology and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mu \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation> its unique measure of maximal entropy. We prove that <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mu \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mu \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation>.</p>

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Exponential mixing of all orders on Kähler manifolds: (quasi-)plurisubharmonic observables

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月26日

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  • Marco Vergamini,
  • Hao Wu

摘要

Let f be a holomorphic automorphism of a compact Kähler manifold with simple action on cohomology and \(\mu \) μ its unique measure of maximal entropy. We prove that \(\mu \) 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 \(\mu \) μ .