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

Robin Kaiser and Ecaterina Sava-Huss

Statistics & Probability Letters, 2024, vol. 209, issue C

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.

Keywords: Rotor walk; Rotor configuration; Recurrence; Abelian sandpile; Stabilization; Sierpiński gasket (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110090

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