Abstract. 
It is an open problem in the study of dynamical systems whether fast decay
of correlations alone is sufficient for the Central Limit Theorem (CLT) to
hold. On the one hand, there are no examples of dynamical systems for
which correlations decay quickly but the CLT fails. On the other, existing
CLT proofs rely on statistical properties much stronger than correlation
decay. In the talk I will discuss a prime class of physically relevant
systems, called Sinai Billiards, and show that a single  bound on
correlations indeed implies the CLT directly. As a byproduct, the CLT is
obtained for observables possessing remarkably little regularity.