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arXiv · 2511.04806

From Brunn-Minkowski to Prékopa-Leindler and Borell-Brascamp-Lieb: discrete inequalities

Peter van Hintum
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Abstract

We consider a general way to obtain Prékopa-Leindler and Borell-Brascamp-Lieb type inequalities from Brunn-Minkowski type inequalities and provide numerous examples. We use the same heuristic to prove a discrete version of the Prékopa-Leindler and Borell-Brascamp-Lieb inequalities for functions over $\mathbb{Z}^d$. These are the functional extensions of the discrete Brunn-Minkowski inequality conjectured by Ruzsa and recently established by Keevash, Tiba, and the author.

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Peter van Hintum. 2026-02-11. From Brunn-Minkowski to Prékopa-Leindler and Borell-Brascamp-Lieb: discrete inequalities. https://arxiv.org/abs/2511.04806

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