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Kaiser, Robin; Sava-Huss, Ecaterina

Random rotor walks and i.i.d. sandpiles on Sierpiński graphs. (English) Zbl 07878509

Stat. Probab. Lett. 209, Article ID 110090, 9 p. (2024).
Summary: We prove that, on the infinite Sierpiński gasket graph \(\mathsf{SG} \), 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 \(\mathsf{SG} \).

MSC:

05C81 Random walks on graphs
60J45 Probabilistic potential theory
60G50 Sums of independent random variables; random walks

Keywords:

rotor walk; rotor configuration; recurrence; abelian sandpile; stabilization; Sierpiński gasket
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Full Text: DOI arXiv

References:

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