Central limit theorem and stable laws for intermittent maps

2002/11/06 by Sébastien Gouëzel, Sebastien Gouezel, Gouezel, Sebastien · 4 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Mathematical Dynamics and Fractals #math.DS #msc:37A30 #msc:37A50 #msc:37C30 #msc:37E05 #msc:47A56 #msc:60F05

paper · pdf · doi:10.48550/arxiv.math/0211117

42 pages

arxiv created 2002/12/06 · arxiv updated 2009/11/30

Abstract

In the setting of abstract Markov maps, we prove results concerning the convergence of renormalized Birkhoff sums to normal laws or stable laws. They apply to one-dimensional maps with a neutral fixed point at 0 of the form x+x^1+α, for α∈ (0,1). In particular, for α>1/2, we show that the Birkhoff sums of a Hölder observable f converge to a normal law or a stable law, depending on whether f(0)=0 or f(0)\not=0. The proof uses spectral techniques introduced by Sarig, and Wiener's Lemma in noncommutative Banach algebras.

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