Truncation of long-range percolation with non-summable interactions in dimensions $d\geq 3$
| Autor: | Bäumler, Johannes |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Consider independent long-range percolation on $\mathbb{Z}^d$ for $d\geq 3$. Assuming that the expected degree of the origin is infinite, we show that there exists an $N\in \mathbb{N}$ such that an infinite open cluster remains after deleting all edges of length at least $N$. For the isotropic case in dimensions $d\geq 3$, we show that if the expected degree of the origin is at least $10^{400}$, then there exists an infinite open cluster almost surely. We also use these results to prove corresponding statements for the long-range $q$-states Potts model. Comment: 41 pages, 1 figure |
| Databáze: | arXiv |
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