The distance problem on measured metric spaces
Probability
2024-03-19 v1 Metric Geometry
Abstract
What distributions arise as the distribution of the distance between two typical points in some measured metric space? This seems to be a surprisingly subtle problem. We conjecture that every distribution with a density function whose support contains does arise in this way, and give some partial results in that direction.
Cite
@article{arxiv.2403.10926,
title = {The distance problem on measured metric spaces},
author = {David J. Aldous and Guillaume Blanc and Nicolas Curien},
journal= {arXiv preprint arXiv:2403.10926},
year = {2024}
}