The distance problem via subadditivity
Probability
2025-07-22 v2 Metric Geometry
Abstract
In a recent paper, Aldous, Blanc and Curien asked which distributions can be expressed as the distance between two independent random variables on some separable measured metric space. We show that every nonnegative discrete distribution whose support contains arises in this way, as well as a class of finitely supported distributions with density.
Cite
@article{arxiv.2501.11445,
title = {The distance problem via subadditivity},
author = {Renan Gross},
journal= {arXiv preprint arXiv:2501.11445},
year = {2025}
}
Comments
10 pages, 2 figures. To appear in Annales Henri Lebesgue