### April 8, 2019

**Pablo Rotondo**(LIGM)

In this talk I will present a probabilistic study of Sturmian words. Sturmian words come up

naturally as discrete codings of irrational lines, and the study of their (finite) factors is of key interest.

In particular, the recurrence function measures the gaps between occurrences of these

factors. During the talk we will give a brief overview of the fundamental facts about Sturmian

words, the classical extreme case results for their recurrence function and finally

our study under a natural probabilistic model.

Based on joint work with Brigitte Vallée (CNRS, Univ. Caen).