Central limit theorem and stable laws for intermittent maps

Details Central limit theorem and stable laws for intermittent maps Central limit theorem and stable laws for intermittent maps

2002-11-06

arxiv.org/abs/math/0211117v2

Mathematics

Dynamical Systems

42 pages

Scientific paper

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 $x+x^{1+\alpha}$, for $\alpha\in (0,1)$. In particular, for $\alpha>1/2$, we show that the Birkhoff sums of a H\"older 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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