Title: A new Central Limit Theorem for Sinai Billiards.
Abstract: It is a long-standing 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 exist no
examples of dynamical systems to date for which correlations decay
quickly but the CLT fails. On the other hand, the CLT proofs in the
literature rely on statistical properties much stronger than
correlation decay. In the talk I will discuss a prime class of a
physically relevant systems, called Sinai Billiards, and show that a
single correlation bound indeed implies the CLT directly. As a
byproduct, the CLT is obtained for observables possessing remarkably
little regularity. The talk will be accessible to a wide audience.