The Logarithmic Sobolev Inequality: Stability, Instability, and Improved Convergence Rates for the Ornstein–Uhlenbeck Flow

par Nikita Simonov (LJLL - Sorbonne Université)

lundi 10 nov. 2025, 14:00 → 15:00 Europe/Paris

Amphi Schwartz

In certain functional inequalities, the best constants and minimizers are known. The next natural question concerns stability: if a function “almost attains equality,” in what sense is it close to a minimizer? We will discuss some recent results (both positive and negative) on quantitative stability for the Logarithmic Sobolev inequality. Our approach is based on a variant of the carré du champ method for the Ornstein–Uhlenbeck equation, enabling us to derive fully constructive estimates. This talk is based on a series of results obtained in collaboration with Giovanni Brigati (ISTA) and Jean Dolbeault (CEREMADE–Dauphine).