A note on ubiquity of geometric Brascamp-Lieb data

TL;DR

This paper demonstrates that geometric Brascamp-Lieb data are widespread, addressing a question about their ubiquity raised in recent work on the adjoint Brascamp-Lieb inequality, by building on prior foundational research.

Contribution

It establishes the widespread presence of geometric Brascamp-Lieb data, answering a key open question in the field.

Findings

Geometric Brascamp-Lieb data are shown to be ubiquitous.

Addresses a question raised by Bennett and Tao.

Builds on foundational work by Garg, Gurvits, Oliveira, and Wigderson.

Abstract

Relying substantially on work of Garg, Gurvits, Oliveira and Wigderson, it is shown that geometric Brascamp--Lieb data are, in a certain sense, ubiquitous. This addresses a question raised by Bennett and Tao in their recent work on the adjoint Brascamp--Lieb inequality.