Work

Gaussian Correlation via Inverse Brascamp–Lieb

Year: 2025

Type: article

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.

Source: Probability Theory and Related Fields

DOI: 10.1007/s00440-025-01445-x

Author: Emanuel Milman

Institution: Technion – Israel Institute of Technology

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: European Commission, Technion-Israel Institute of Technology, European Research Council