Mean Width of Random Perturbations of Random Polytopes

TL;DR

This paper investigates the expected mean width of randomly perturbed polytopes under various distributions, providing high probability bounds for Gaussian, p-stable, and uniform cases.

Contribution

It offers new high probability results on the mean width of perturbed random polytopes for multiple probability distributions, extending existing geometric analysis.

Findings

Expected mean width bounds for Gaussian perturbations

Expected mean width bounds for p-stable perturbations

Results for uniform distributions on $\,\ell_p^N$-balls and spheres

Abstract

We prove some "high probability" results on the expected value of the mean width for random perturbations of random polytopes. The random perturbations are considered for Gaussian and $p$-stable random vectors, as well as uniform distributions on $\ell_p^N$-balls and the unit sphere.