An Invariance Principle for Maps with Polynomial Decay of Correlations

2004/08/13 by Marta Tyran‐Kamińska, Marta Tyran-Kaminska · 1 citation
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.DS #msc:37A50 #msc:37D20 #msc:60F17

paper · pdf · doi:10.1007/s00220-005-1400-z

published as Comm. Math. Phys. 260 (2005) 1-15 · 15 pages

arxiv created 2004/08/13 · openalex publication_date 2005/08/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We give a general method of deriving statistical limit theorems, such as the central limit theorem and its functional version, in the setting of ergodic measure preserving transformations. This method is applicable in situations where the iterates of discrete time maps display a polynomial decay of correlations.

Citations

• Recurrence times and rates of mixing
• GIBBS MEASURES IN ERGODIC THEORY
• Statistical Properties of Dynamical Systems with Some Hyperbolicity
• On mixing properties of compact group extensions of hyperbolic systems
• Decay of correlations, central limit theorems and approximation by Brownian motion for compact Lie group extensions

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