Voronoi Percolation: Topological Stability and Giant Cycles
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915704682315776 |
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| author | Schweinhart, Benjamin Shuman, Morgan |
| author_facet | Schweinhart, Benjamin Shuman, Morgan |
| contents | We study the topological stability of Voronoi percolation in higher dimensions. We show that slightly increasing p allows a discretization that preserves increasing topological properties with high probability. This strengthens a theorem of Bollobás and Riordan and generalizes it to higher dimensions. As a consequence, we prove a sharp phase transition for the emergence of i-dimensional giant cycles in Voronoi percolation on the 2i-dimensional torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00793 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Voronoi Percolation: Topological Stability and Giant Cycles Schweinhart, Benjamin Shuman, Morgan Probability Mathematical Physics Algebraic Topology We study the topological stability of Voronoi percolation in higher dimensions. We show that slightly increasing p allows a discretization that preserves increasing topological properties with high probability. This strengthens a theorem of Bollobás and Riordan and generalizes it to higher dimensions. As a consequence, we prove a sharp phase transition for the emergence of i-dimensional giant cycles in Voronoi percolation on the 2i-dimensional torus. |
| title | Voronoi Percolation: Topological Stability and Giant Cycles |
| topic | Probability Mathematical Physics Algebraic Topology |
| url | https://arxiv.org/abs/2601.00793 |