Decay of correlations, central limit theorems and approximation by Brownian motion for compact Lie group extensions

2003/01/16 by Michael Field, MICHAEL FIELD, IAN MELBOURNE +3 · 1 citation
Mathematics · #Functional Equations Stability Results #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · doi:10.1017/s0143385702000901

openalex publication_date 2003/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25

Abstract

Hölder continuous observations on hyperbolic basic sets satisfy strong statistical properties such as exponential decay of correlations, central limit theorems and invariance principles (approximation by Brownian motion).Using an equivariant version of the Ruelle transfer operator studied by Parry and Pollicott, we obtain similar results for equivariant observations on compact group extensions of hyperbolic basic sets.

Citations

• Almost sure invariance principles for partial sums of weakly dependent random variables
• Foundations of Modern Probability
• On mixing properties of compact group extensions of hyperbolic systems

Cited by

• Extremal Lyapunov exponents in random dynamics

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• The central limit theorem on nilpotent Lie groups
• Statistical limit laws for hyperbolic groups
• Decay of Correlations for Partially Hyperbolic Skew-Products
• Counting and boundary limit theorems for representations of Gromov-hyperbolic groups
• Integration formulas for Brownian motion on classical compact Lie groups