On the isotropy constant of projections of polytopes

TL;DR

This paper establishes an upper bound on the isotropy constant of d-dimensional polytopes with n vertices, showing it is at most proportional to the square root of n over d, with a universal constant.

Contribution

It provides a new universal bound on the isotropy constant of polytopes based on their vertices and dimension, advancing understanding of geometric properties of polytopes.

Findings

Isotropy constant bounded by C√(n/d) for polytopes with n vertices

Universal constant C independent of polytope specifics

Improves bounds on geometric measures of polytopes

Abstract

The isotropy constant of any $d$-dimensional polytope with $n$ vertices is bounded by $C \sqrt{n/d}$ where $C>0$ is a numerical constant.