Orateur
Noé Cuneo
(Université Paris Cité)
Description
Once the sequence $(n^{-1}\ln R_n)$ of return times introduced in Renaud's talk has been shown to satisfy a law of large numbers, a natural question is to study its large deviations. Quite surprisingly, very limited results were available. In a recent paper with Renaud Raquépas, we proved that the return times satisfy the full large deviation principle, again under some quite mild decoupling assumptions. I will present this result and outline the proof. As we will show, we find a natural expression for the large-deviation rate function. Moreover, if the definition of $R_n$ allows for some "overlaps", we will see that the rate function is nonconvex in general.
