Stabilizability and percolation in the infinite volume sandpile model
Stabilizability and percolation in the infinite volume sandpile model
复制标题
无限体积沙堆模型的稳定性和渗流
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
F. Redig
中科院分区：
文献类型：
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作者：
A. Fey;R. Meester;F. Redig
我们研究Z d 上无限体积的沙堆模型。特别是，我们感兴趣的问题是，根据固定测量 μ 选择的初始配置是否 μ 几乎肯定是稳定的。我们证明稳定性并不取决于我们采用的特定稳定程序。在 d = 1 和 μ 的乘积测量中，密度 ρ = 1（d = 1 中稳定性的已知临界值）以及空位点的正密度，我们证明 μ 是不可稳定的。此外，我们研究了 p 的值使得 μ 是稳定的，倾倒地点的渗透。我们发现，当 p > 0 足够小时，存在一个亚临界状态，其中一群倒塌位点的分布具有指数尾部，就像普通渗流的亚临界状态中的情况一样。
We study the sandpile model in infinite volume on Z d . In particular, we are interested in the question whether or not initial configurations, chosen according to a stationary measure μ, are μ-almost surely stabilizable. We prove that stabilizability does not depend on the particular procedure of stabilization we adopt. In d = 1 and μ a product measure with density ρ = 1 (the known critical value for stabilizability in d = 1) with a positive density of empty sites, we prove that μ is not stabilizable. Furthermore, we study, for values of p such that μ is stabilizable, percolation of toppled sites. We find that for p > 0 small enough, there is a subcritical regime where the distribution of a cluster of toppled sites has an exponential tail, as is the case in the subcritical regime for ordinary percolation.