Thresholds for geometric graphs
Fuente:
arXiv
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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917517295878144 |
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| author | Narayanan, Bhargav |
| author_facet | Narayanan, Bhargav |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21480 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Thresholds for geometric graphs Narayanan, Bhargav Combinatorics Metric Geometry Probability Primary 05C80, Secondary 52A40, 60D05, 37A30 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. |
| title | Thresholds for geometric graphs |
| topic | Combinatorics Metric Geometry Probability Primary 05C80, Secondary 52A40, 60D05, 37A30 |
| url | https://arxiv.org/abs/2605.21480 |