Central limit theorem and stable laws for intermittent maps

Original · EN

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+x¹⁺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)=0. The proof uses spectral techniques introduced by Sarig, and Wiener's Lemma in noncommutative Banach algebras.