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Random rotor walks and i.i.d. sandpiles on Sierpiński graphs

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  • Kaiser, Robin
  • Sava-Huss, Ecaterina

Abstract

We prove that, on the infinite Sierpiński 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.

Suggested Citation

  • Kaiser, Robin & Sava-Huss, Ecaterina, 2024. "Random rotor walks and i.i.d. sandpiles on Sierpiński graphs," Statistics & Probability Letters, Elsevier, vol. 209(C).
    • Handle: RePEc:eee:stapro:v:209:y:2024:i:c:s0167715224000592
    DOI: 10.1016/j.spl.2024.110090
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    References listed on IDEAS

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    1. Daerden, F. & Priezzhev, V.B. & Vanderzande, C., 2001. "Waves in the sandpile model on fractal lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 292(1), pages 43-54.
    2. Daerden, Frank & Vanderzande, Carlo, 1998. "Sandpiles on a Sierpinski gasket," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 256(3), pages 533-546.
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