The stability of log-supermodularity under convolution
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914213867290624 |
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| author | Madiman, Mokshay Melbourne, James Roberto, Cyril |
| author_facet | Madiman, Mokshay Melbourne, James Roberto, Cyril |
| contents | We study the behavior of log-supermodular functions under convolution. In particular we show that log-concave product densities preserve log-supermodularity, confirming in the special case of the standard Gaussian density, a conjecture of Zartash and Robeva. Additionally, this stability gives a ``conditional'' entropy power inequality for log-supermodular random variables. We also compare the Ahlswede-Daykin four function theorem and a recent four function version of the Prekopa-Leindler inequality due to Cordero-Erausquin and Maurey and giving transport proofs for the two theorems. In the Prekopa-Leindler case, the proof gives a generalization that seems to be new, which interpolates the classical three and the recent four function versions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19003 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The stability of log-supermodularity under convolution Madiman, Mokshay Melbourne, James Roberto, Cyril Probability Information Theory Functional Analysis We study the behavior of log-supermodular functions under convolution. In particular we show that log-concave product densities preserve log-supermodularity, confirming in the special case of the standard Gaussian density, a conjecture of Zartash and Robeva. Additionally, this stability gives a ``conditional'' entropy power inequality for log-supermodular random variables. We also compare the Ahlswede-Daykin four function theorem and a recent four function version of the Prekopa-Leindler inequality due to Cordero-Erausquin and Maurey and giving transport proofs for the two theorems. In the Prekopa-Leindler case, the proof gives a generalization that seems to be new, which interpolates the classical three and the recent four function versions. |
| title | The stability of log-supermodularity under convolution |
| topic | Probability Information Theory Functional Analysis |
| url | https://arxiv.org/abs/2512.19003 |