可分沙堆模型的里程计：标度极限、iDLA和障碍问题。一项调查
Odometers of Divisible Sandpile Models: Scaling Limits, iDLA and Obstacle Problems. A Survey
摘要：
可分沙堆模型是阿贝尔沙堆模型的固定能量连续对应模型。我们从一个随机的初始构型开始，确定性地重新分配质量。在一定条件下沙堆会稳定下来。相关的里程表函数描述了稳定过程中从每个顶点发射的质量。在这项调查中，我们描述了最近的缩放限制结果的里程表功能取决于不同的初始配置和重新分配规则。此外，我们审查连接的障碍问题，从位势论，包括里程表和极限形状的增长模型，如iDLA之间的连接。最后提出了一些有待解决的问题。
英文摘要：
The divisible sandpile model is a fixed-energy continuous counterpart of the Abelian sandpile model. We start with a random initial configuration and redistribute mass deterministically. Under certain conditions the sandpile will stabilize. The associated odometer function describes the amount of mass emitted from each vertex during stabilization. In this survey we describe recent scaling limit results of the odometer function depending on different initial configurations and redistribution rules. Moreover we review connections to the obstacle problem from potential theory, including the connection between odometers and limiting shapes of growth models such as iDLA. Finally we state some open problems.
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