Gaussian concentration bounds and finitary coding
Event details
| Date | 26.03.2025 |
| Hour | 16:15 › 17:15 |
| Speaker | Sandro Gallo, Universide Federal de São Carlos (Brazil) |
| Location | |
| Category | Conferences - Seminars |
| Event Language | English |
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 relate the occurrence of such bounds to the concept of finitary coding (or factor) coming from dynamical systems. As a consequence, I will present recent results establishing gaussian concentration bounds for a wide class of random fields on $\mathds{Z}^d$, in particular the Ising model above the critical temperature in any dimension.
This presentation is based on joint work with Jean-René Chazottes (CNRS & École Polytechnique, Palaiseau) and Daniel Y. Takahashi (Instituto do Cérebro, UFRN, Brazil).
-- A Probability and Stochastic Analysis Seminar--
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