Quantitative stability for the Brascamp–Lieb inequality and moment measures

par Joao Machado (LMCRC Huawei)

mercredi 1 juil. 2026, 10:30 → 11:30 Europe/Paris

112 (Braconnier)

In this talk, we present recent results on quantitative stability for the Brascamp–Lieb inequality, around the variance with respect to a log-concave measure. Several proofs of this inequality are known in the literature. Classical approaches rely in particular on the Bakry–Émery Γ-calculus, while others, such as that of Bobkov and Ledoux (2000), are based on the Prékopa–Leindler inequality.

We explain how the optimal quantitative stability version of the Prékopa–Leindler inequality obtained by Figalli, van Hintum, and Tiba (2025) can be combined with the theory of moment measures to strengthen the Bobkov–Ledoux proof strategy. This approach yields a quantitative stability version of the Brascamp–Lieb inequality with several remarkable properties: optimality of the stability exponent and a constant depending only on the dimension.

In particular, this constant is universal over the class of log-concave measures with essentially continuous convex potentials. This minimal regularity assumption on the convex potential is optimal to ensure non-degeneracy of the associated moment measure, as shown by Cordero-Erausquin and Klartag (2015). Finally, we discuss how this result can be used to understand quantitative stability for moment measures themselves, highlighting the close links between these two problems.

This is joint work with João Pedro Ramos: https://arxiv.org/abs/2511.22636