Student Probability Seminar

---

Limit theorems for recurrence times on one-sided shifts

Speaker: Renaud Raquépas, CIMS

Location: Warren Weaver Hall 1314

Date: Monday, March 27, 2023, 1:15 p.m.

Synopsis:

Poincaré’s theorem and Kac’s lemma on recurrence times are basic results that one typically encounters quite early on when studying dynamical systems. Perhaps less well known is a 1993 result of Ornstein and Weiss on the time it takes for the n first symbols in a sequence sampled from an ergodic measure P on a one-sided shift to reappear down this same sequence: they build on ideas of Wyner and Ziv to relate, P-almost surely, the growth rate in n of these recurrence times to the entropy of the measure P. With Noé Cuneo (Paris Cité), I am currently finishing a paper on the LDP accompanying this LLN. While part of the appeal of our result is the generality of the class of measures P to which it applies, I believe that important ideas can be conveyed using the simple set-up of irreducible and aperiodic Markov chains.