# On the ℓ0 Isoperimetric Coefficient of Measurable Sets

arXiv: https://arxiv.org/abs/2312.00015 · HTML: https://mlsanity.com/paper/2312.00015/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2023.

## Built on by (most cited first, 1 of 1)

- [A mixing time bound for Gibbs sampling from log-smooth log-concave distributions](https://mlsanity.com/paper/2412.17899/) (2024)

## Abstract (arXiv)

In this paper we prove that the ℓ0 isoperimetric coefficient for any axis-aligned cubes, psiC, is Theta(n-1/2) and that the isoperimetric coefficient for any measurable body K, psiK, is of order O(n-1/2). As a corollary we deduce that axis-aligned cubes essentially "maximize" the ℓ0 isoperimetric coefficient: There exists a positive constant q > 0 such that psiK ≤ q · psiC, whenever C is an axis-aligned cube and K is any measurable set. Lastly, we give immediate applications of our results to the mixing time of Coordinate-Hit-and-Run for sampling points uniformly from convex bodies.