论文标题
Edgeworth扩展，用于覆盖多项式体积增长图的中心随机步行
Edgeworth expansions for centered random walks on covering graphs of polynomial volume growth
论文作者
论文摘要
在几个自然假设下，获得了带有多项式体积生长组的覆盖图上随机步行的Edgeworth扩展。在此扩展中出现的系数不仅取决于基础图的几何特征，还取决于该图的修改后的谐波嵌入到某个nilpotent Lie组中。此外，我们将收敛速率应用于Trotter的近似定理中，以建立用于随机步行的Berry-Esseen类型。
Edgeworth expansions for random walks on covering graphs with groups of polynomial volume growths are obtained under a few natural assumptions. The coefficients appearing in this expansion depends on not only geometric features of the underlying graphs but also the modified harmonic embedding of the graph into a certain nilpotent Lie group. Moreover, we apply the rate of convergence in Trotter's approximation theorem to establish the Berry-Esseen type bound for the random walks.
