Abstract
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.
| Original language | English GB |
|---|---|
| Journal | Probability Theory and Related Fields |
| DOIs | |
| State | Accepted/In press - 2025 |
Keywords
- Even log-concave functions
- Gaussian correlation inequality
- Inverse Brascamp–Lieb inequality
ASJC Scopus subject areas
- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty
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