$L^2$-stability for the variance Brascamp-Lieb inequality

TL;DR

This paper establishes an $L^2$-stability estimate for the variance Brascamp-Lieb inequality by leveraging recent $L^1$-stability results and introducing a new super-Brascamp-Lieb inequality assumption.

Contribution

It introduces an $L^2$-stability estimate for the variance Brascamp-Lieb inequality using a novel bootstrap approach and a new super-Brascamp-Lieb inequality assumption.

Findings

Proves an $L^2$-stability estimate for the variance Brascamp-Lieb inequality.

Introduces the super-Brascamp-Lieb inequality as a key assumption.

Connects $L^1$-stability results to $L^2$-stability through bootstrap methods.

Abstract

We prove an $L^2$-stability estimate for the variance Brascamp-Lieb inequality [J. Funct. Anal. 22 (4), 366-389 (1976)] by bootstrapping the recent $L^1$-stability theorem of Machado and Ramos [arXiv:2511.22636] under an additional assumption, which we call the super-Brascamp-Lieb inequality, of independent interest.