From Brunn-Minkowski to Prékopa-Leindler and Borell-Brascamp-Lieb: discrete inequalities
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910018322825216 |
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| author | van Hintum, Peter |
| author_facet | van Hintum, Peter |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04806 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Brunn-Minkowski to Prékopa-Leindler and Borell-Brascamp-Lieb: discrete inequalities van Hintum, Peter Combinatorics Classical Analysis and ODEs Functional Analysis Metric Geometry 52A40, 49Q22, 26D15, 26D20, 11P70 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. |
| title | From Brunn-Minkowski to Prékopa-Leindler and Borell-Brascamp-Lieb: discrete inequalities |
| topic | Combinatorics Classical Analysis and ODEs Functional Analysis Metric Geometry 52A40, 49Q22, 26D15, 26D20, 11P70 |
| url | https://arxiv.org/abs/2511.04806 |