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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.01122 |
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Table of Contents:
- We consider the problem of stability for the Prékopa-Leindler inequality. Exploiting properties of the transport map between radially decreasing functions and a suitable functional version of the trace inequality, we obtain a uniform stability exponent for the Prékopa-Leindler inequality. Our result yields an exponent not only uniform in the dimension but also in the log-concavity parameter $τ= \min(λ,1-λ)$ associated with its respective version of the Prékopa-Leindler inequality. As a further application of our methods, we prove a sharp stability result for log-concave functions in dimension 1, which also extends to a sharp stability result for log-concave radial functions in higher dimensions.