Central limit theorem and stable laws for intermittent maps

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 alphais an element of(0, 1). In particular, for alpha>1/2, we show that the Birkhoff sums of a Holder observable f converge to a normal law or a stable law, depending on whether f(0)=0 or f(0)not equal0. The proof uses spectral techniques introduced by Sarig, and Wiener's Lemma in non-commutative Banach algebras.