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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.07601 |
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| _version_ | 1866915942586384384 |
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| author | Marcolli, Matilde |
| author_facet | Marcolli, Matilde |
| contents | Models of long range percolations on lattices and on hierarchical lattices are related through the use of three intermediate geometries: a 1-parameter deformation based on the power mean function, relating lattice percolation to a percolation model governed by the toric volume form; the adelic product formula for a function field, relating the hierarchical lattice model to an adelic percolation model; and the adelic product formula for number fields that relates the toric percolation model on the lattice given by the ring of integers in the Minkowski embedding to another adelic percolation model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07601 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adelic Models of Percolation Marcolli, Matilde Mathematical Physics Number Theory Probability 60K35, 82B43, 11F85, 37P20, 11R59, 11R42 Models of long range percolations on lattices and on hierarchical lattices are related through the use of three intermediate geometries: a 1-parameter deformation based on the power mean function, relating lattice percolation to a percolation model governed by the toric volume form; the adelic product formula for a function field, relating the hierarchical lattice model to an adelic percolation model; and the adelic product formula for number fields that relates the toric percolation model on the lattice given by the ring of integers in the Minkowski embedding to another adelic percolation model. |
| title | Adelic Models of Percolation |
| topic | Mathematical Physics Number Theory Probability 60K35, 82B43, 11F85, 37P20, 11R59, 11R42 |
| url | https://arxiv.org/abs/2508.07601 |