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arXiv · 2605.21480

Thresholds for geometric graphs

Bhargav Narayanan
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Abstract

A metric probability space $M$ admits thresholds if the random geometric graph on $M$ has a threshold for every monotone graph property. We connect the existence of thresholds to the uniform expansion of $M$ and prove that all standard tori, spheres, and cubes admit thresholds.

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Bhargav Narayanan. 2026-05-20. Thresholds for geometric graphs. https://arxiv.org/abs/2605.21480

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