On the structure of the sandpile identity element on Sierpinski gasket graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910050617917440 |
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| author | Kaiser, Robin Sava-Huss, Ecaterina Überbacher, Julia |
| author_facet | Kaiser, Robin Sava-Huss, Ecaterina Überbacher, Julia |
| contents | We consider the identity of the abelian sandpile group of finite approximation graphs of the Sierpinski gasket, and we show that the second-order term in the scaling limit converges to the path distance to the nearest corner on the Sierpinski gasket. The proof relies on a decomposition of the identity of the sandpile group into the sum of a constant function and the Laplacian of the graph distance on the approximating graphs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_12006 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the structure of the sandpile identity element on Sierpinski gasket graphs Kaiser, Robin Sava-Huss, Ecaterina Überbacher, Julia Combinatorics Probability 31E05, 60J10, 60J45, 05C81 We consider the identity of the abelian sandpile group of finite approximation graphs of the Sierpinski gasket, and we show that the second-order term in the scaling limit converges to the path distance to the nearest corner on the Sierpinski gasket. The proof relies on a decomposition of the identity of the sandpile group into the sum of a constant function and the Laplacian of the graph distance on the approximating graphs. |
| title | On the structure of the sandpile identity element on Sierpinski gasket graphs |
| topic | Combinatorics Probability 31E05, 60J10, 60J45, 05C81 |
| url | https://arxiv.org/abs/2603.12006 |