English

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 00 does arise in this way, and give some partial results in that direction.

Keywords

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}
}
R2 v1 2026-06-28T15:22:47.755Z