Random rotor walks and i.i.d. sandpiles on Sierpinski graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| author | Kaiser, Robin Sava-Huss, Ecaterina |
| author_facet | Kaiser, Robin Sava-Huss, Ecaterina |
| contents | We prove that, on the infinite Sierpinski gasket graph SG, rotor walk with random initial configuration of rotors is recurrent. We also give a necessary condition for an i.i.d. sandpile to stabilize. In particular, we prove that an i.i.d. sandpile with expected number of chips per site greater or equal to three does not stabilize almost surely. Furthermore, the proof also applies to divisible sandpiles and shows that divisible sandpile at critical density one does not stabilize almost surely on SG. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_00810 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Random rotor walks and i.i.d. sandpiles on Sierpinski graphs Kaiser, Robin Sava-Huss, Ecaterina Probability Combinatorics 60J10, 60J45, 05C81 We prove that, on the infinite Sierpinski gasket graph SG, rotor walk with random initial configuration of rotors is recurrent. We also give a necessary condition for an i.i.d. sandpile to stabilize. In particular, we prove that an i.i.d. sandpile with expected number of chips per site greater or equal to three does not stabilize almost surely. Furthermore, the proof also applies to divisible sandpiles and shows that divisible sandpile at critical density one does not stabilize almost surely on SG. |
| title | Random rotor walks and i.i.d. sandpiles on Sierpinski graphs |
| topic | Probability Combinatorics 60J10, 60J45, 05C81 |
| url | https://arxiv.org/abs/2210.00810 |