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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.11018 |
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| _version_ | 1866908617619275776 |
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| author | Milman, Emanuel |
| author_facet | Milman, Emanuel |
| contents | We give a simple alternative proof of Royen's Gaussian Correlation inequality by using (a slightly generalized version of) Nakamura-Tsuji's symmetric inverse Brascamp-Lieb inequality for even log-concave functions. We explain that this inverse inequality is in a certain sense a dual counterpart to the forward inequality of Bennett-Carbery-Christ-Tao and Valdimarsson, and that the log-concavity assumption therein cannot be omitted in general. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11018 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gaussian Correlation via Inverse Brascamp-Lieb Milman, Emanuel Functional Analysis Probability We give a simple alternative proof of Royen's Gaussian Correlation inequality by using (a slightly generalized version of) Nakamura-Tsuji's symmetric inverse Brascamp-Lieb inequality for even log-concave functions. We explain that this inverse inequality is in a certain sense a dual counterpart to the forward inequality of Bennett-Carbery-Christ-Tao and Valdimarsson, and that the log-concavity assumption therein cannot be omitted in general. |
| title | Gaussian Correlation via Inverse Brascamp-Lieb |
| topic | Functional Analysis Probability |
| url | https://arxiv.org/abs/2501.11018 |