论文标题
随机转子步行和I.I.D. sierpinski图上的沙珀
Random rotor walks and i.i.d. sandpiles on Sierpinski graphs
论文作者
论文摘要
我们证明，在无限的Sierpinski垫圈图SG上，转子步行带有随机的转子初始配置，这是经常性的。我们还为I.I.D提供了必要的条件沙珀稳定。特别是，我们证明了I.I.D.每个位置的预期芯片数量更大或等于三的碎片肯定不会稳定。此外，该证明也适用于可划分的沙板，并表明在临界密度下可划分的沙板几乎不能肯定地稳定在SG上。
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.
