The return time picture for stationary processes was originally addressed by Poincaré with his famous recurrence theorem. In the case of rare events (events of small measure), it is naturally associated to long time behavior, since the Kac Lemma states that the expected return time to a set is the inverse of the measure of the set. It is now well understood that the short time behavior, through the control of the probability of “as soon as possible”-returns to the set, plays a fundamental role in the Poincaré recurrence theory. The main objective of the talk will be to explain how this probability of “soon” returns shows up in the calculations an

Pontifical Catholic University of Chile (PUC-Chile)

Av. Vicuña Mackenna 4860, Macul,

Santiago – Chile

(+56 2) 2354 5779

Faculty of Physical and Mathematical Sciences (FCFM)

Universidad de Chile

Beauchef 851, Edificio Norte, Piso 7,

Santiago – Chile