Average height for Abelian sandpiles and the looping constant on Sierpinski graphs
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866929699269115904 |
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| author | Heizmann, Nico Kaiser, Robin Sava-Huss, Ecaterina |
| author_facet | Heizmann, Nico Kaiser, Robin Sava-Huss, Ecaterina |
| contents | For the Abelian sandpile model on Sierpinski graphs, we investigate several statistics such as average height, height probabilities and looping constant. In particular, we calculate the expected average height of a recurrent sandpile on the finite iterations of the Sierpinski gasket and we also give an algorithmic approach for calculating the height probabilities of recurrent sandpiles under stationarity by using the connection between recurrent configurations of the Abelian sandpile Markov chain and uniform spanning trees. We also calculate the expected fraction of vertices of height $i$ for $i\in\{0,1,2,3\}$ of sandpiles under stationarity and relate the bulk average height to the looping constant on the Sierpinski gasket. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_03445 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Average height for Abelian sandpiles and the looping constant on Sierpinski graphs Heizmann, Nico Kaiser, Robin Sava-Huss, Ecaterina Probability Combinatorics 60J10, 60J45, 05C81, 31E05 For the Abelian sandpile model on Sierpinski graphs, we investigate several statistics such as average height, height probabilities and looping constant. In particular, we calculate the expected average height of a recurrent sandpile on the finite iterations of the Sierpinski gasket and we also give an algorithmic approach for calculating the height probabilities of recurrent sandpiles under stationarity by using the connection between recurrent configurations of the Abelian sandpile Markov chain and uniform spanning trees. We also calculate the expected fraction of vertices of height $i$ for $i\in\{0,1,2,3\}$ of sandpiles under stationarity and relate the bulk average height to the looping constant on the Sierpinski gasket. |
| title | Average height for Abelian sandpiles and the looping constant on Sierpinski graphs |
| topic | Probability Combinatorics 60J10, 60J45, 05C81, 31E05 |
| url | https://arxiv.org/abs/2308.03445 |