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arXiv · 2403.10926

The distance problem on measured metric spaces

David J. Aldous·Guillaume Blanc·Nicolas Curien
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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 $0$ does arise in this way, and give some partial results in that direction.

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David J. Aldous, Guillaume Blanc, Nicolas Curien. 2024-03-16. The distance problem on measured metric spaces. https://arxiv.org/abs/2403.10926

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