Séminaire de Probabilités et Statistique
Monday 23 June 2025 à 13:45 - UM - Bât 09 - Salle de conférence (1er étage)
Sandro Gallo (Université fédérale de São Carlos, Brésil)
Gaussian concentration bounds for stochastic processes
The study of concentration inequalities focuses on upper bounds for the probability that certain statistics of (fixed-size) random samples deviate significantly from their mean (or median). For i.i.d. samples, what we refer to as a "Gaussian concentration bound" is a specific case of a concentration inequality, commonly known in the literature as McDiarmid’s inequality. More broadly, such bounds are expected to hold for well-behaved statistics (e.g., Lipschitz continuous functions) and for samples of weakly dependent random variables.
In this talk I will: (1) present a method based on the concept of finitary coding to obtain such bounds for a large class of processes and (2) give two specific examples of application: the plug-in estimator of the entropy and Dvoretzky-Kiefer-Wolfowitz-type inequality.
This presentation is based on joint works with Jean-René Chazottes (CNRS & École Polytechnique, Palaiseau) and Daniel Y. Takahashi (Instituto do Cérebro, UFRN, Brazil).
ATTENTION : Séminaire exceptionnellement en salle 430 (4e étage du bâtiment 9), également retransmis sur zoom : https://umontpellier-fr.zoom.us/j/7156708132