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arXiv · 2512.08454

On the stochastic proof of the Blaschke-Santal\'o inequality

Joseph Lehec
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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 Pr\'ekopa-Leindler inequality. The symmetrized Talagrand inequality can be seen as a dual form of the functional Santal\'o 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 Santal\'o inequality directly, rather than in its dual form.

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Joseph Lehec. 2025-12-09. On the stochastic proof of the Blaschke-Santal\'o inequality. https://arxiv.org/abs/2512.08454

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