On the stochastic proof of the Blaschke–Santaló inequality
Abstract
In 2024, Courtade, Fathi and Mikulincer gave a proof of the symmetrized Talagrand inequality based on stochastic calculus, in the spirit of Borell’s proof of the Prékopa–Leindler inequality. The symmetrized Talagrand inequality can be seen as a dual form of the functional Santaló inequality. The modest purpose of this note is to give a simplified version of the Courtade, Fathi and Mikulincer argument. Namely we first recall briefly Borell’s original argument, and we then explain a simple twist in his proof that allows to recover the functional Santaló inequality directly, rather than in its dual form.
Fields of Study & Subjects
Mathematical Inequalities and Applications
Point processes and geometric inequalities
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Comptes Rendus Mathématique
- Volume
- 364
- Issue
- G3
- Pages
- 599–604
- Publication date
- 22 July 2026
- Language
- EN