On the Continuity of Enhancement Percolation
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914064504979456 |
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| author | Duncan, Paul Schweinhart, Benjamin Sivakoff, David |
| author_facet | Duncan, Paul Schweinhart, Benjamin Sivakoff, David |
| contents | We study bond percolation in $\mathbb{Z}^d$ with an unbounded family of enhancements that enable additional bonds to act as open. A natural question is whether percolation occurs in this model if and only if percolation also occurs in the system with a finite subcollection of enhancements. We give an affirmative answer in dimension $d=2$ for symmetric families of connected enhancements, and in dimensions $d\ge 3$ we prove a partial result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10990 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Continuity of Enhancement Percolation Duncan, Paul Schweinhart, Benjamin Sivakoff, David Probability We study bond percolation in $\mathbb{Z}^d$ with an unbounded family of enhancements that enable additional bonds to act as open. A natural question is whether percolation occurs in this model if and only if percolation also occurs in the system with a finite subcollection of enhancements. We give an affirmative answer in dimension $d=2$ for symmetric families of connected enhancements, and in dimensions $d\ge 3$ we prove a partial result. |
| title | On the Continuity of Enhancement Percolation |
| topic | Probability |
| url | https://arxiv.org/abs/2509.10990 |