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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.20329 |
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| _version_ | 1866917036292046848 |
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| author | Reani, Yohai Bobrowski, Omer |
| author_facet | Reani, Yohai Bobrowski, Omer |
| contents | We introduce a novel approach for studying random k-coverage, using Morse theory for the k-nearest neighbor (k-NN) distance function. We prove a sharp phase transition for the number of critical points of the k-NN distance function, from which we conclude a phase transition for k-coverage. In addition, in the critical window our new framework enables us to prove a Poisson process approximation (in both location and size) for the last uncovered regions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20329 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp Phase Transitions for k-Fold Coverage Using Morse Theory Reani, Yohai Bobrowski, Omer Probability Algebraic Topology 60D05, 60G55, 60G70, 60B99 We introduce a novel approach for studying random k-coverage, using Morse theory for the k-nearest neighbor (k-NN) distance function. We prove a sharp phase transition for the number of critical points of the k-NN distance function, from which we conclude a phase transition for k-coverage. In addition, in the critical window our new framework enables us to prove a Poisson process approximation (in both location and size) for the last uncovered regions. |
| title | Sharp Phase Transitions for k-Fold Coverage Using Morse Theory |
| topic | Probability Algebraic Topology 60D05, 60G55, 60G70, 60B99 |
| url | https://arxiv.org/abs/2510.20329 |