In their previous work, the authors studied the abelian sandpile model on graphs constructed from a growing piece of a plane or space tiling, given periodic or open boundary conditions, and identified spectral factors which govern the asymptotic spectral gap and asymptotic mixing time. This article gives a general method of determining the spectral factor either computationally or asymptotically and performs the determination in specific examples.

中文翻译：

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阿贝尔沙堆模型的频谱

在他们之前的工作中，作者在给定周期性或开放边界条件的情况下，研究了由平面或空间平铺的增长部分构建的图上的阿贝尔沙堆模型，并确定了控制渐近光谱间隙和渐近混合时间的光谱因素。本文给出了计算或渐近确定频谱因子的一般方法，并在具体例子中进行了确定。