Boundary conditions in Abelian sandpiles
Boundary conditions in Abelian sandpiles
复制标题
阿贝尔沙堆的边界条件
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Samuel L. Gamlin
中科院分区：
文献类型：
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作者：
Samuel L. Gamlin
本论文的重点是研究阿贝尔沙堆模型中边界条件对构形的影响。在这篇论文中，我们有两个主要的结果。首先，我们给出了一族从连线生成森林到递归沙堆的连续、保测度、几乎一一映射。在特殊的情况下，$Z^d$，$d geq 2$，我们如何产生这些双射的收敛速度上界的沙堆措施沿着任何用尽$Z^d$。其次，我们考虑了梯形图上的阿贝尔沙堆。对于阶梯沙堆措施，
u$，边界上的递归配置，I，和圆柱事件，E，我们提供了一个上界$
u（E| I）−
u（E）$。
The focus of this thesis is to investigate the impact of the boundary conditions on configurations in the Abelian sandpile model. We have two main results to present in this thesis. Firstly we give a family of continuous, measure preserving, almost one-to-one mappings from the wired spanning forest to recurrent sandpiles. In the special case of $Z^d$, $d geq 2$, we show how these bijections yield a power law upper bound on the rate of convergence to the sandpile measure along any exhaustion of $Z^d$. Secondly we consider the Abelian sandpile on ladder graphs. For the ladder sandpile measure, $
u$, a recurrent configuration on the boundary, I, and a cylinder event, E, we provide an upper bound for $
u(E|I) −
u(E)$.