Abstract Moderate deviation principles (MDPs) for random walks on covering graphs with groups of polynomial volume growth are discussed in a geometric point of view. They deal with any intermediate spatial scalings between those of laws of large numbers and those of central limit theorems. The corresponding rate functions are given by quadratic forms determined by the Albanese metric associated with the given random walks. We apply MDPs to establish laws of the iterated logarithm on the covering graphs by characterizing the set of all limit points of the normalized random walks.

中文翻译：

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多项式体积增长组覆盖图的迭代对数定律

摘要 从几何的角度讨论了在具有多项式体积增长组的覆盖图上随机游走的中度偏差原则 (MDP)。它们处理大数定律和中心极限定理之间的任何中间空间尺度。相应的速率函数由二次形式给出，由与给定随机游走相关的 Albanese 度量确定。我们通过表征归一化随机游走的所有极限点的集合，应用 MDP 在覆盖图上建立迭代对数定律。