标题： 通过Skorohod估计和$p$-Poincaré不等式在泊松空间上的定量CLTs 显示英文标题

标题： Quantitative CLTs on the Poisson space via Skorohod estimates and $p$-Poincaré inequalities

摘要： 我们建立了基于Skorohod积分矩的新估计的泊松泛函高斯逼近的新显式界限。 将这些与Malliavin-Stein方法结合，我们推导了Wasserstein和Kolmogorov距离中的界限，其应用只需要对加一成本算子$\unicode{x2014}$的最小矩假设，从而扩展了(Last, Peccati和Schulte, 2016)的结果。 我们的应用包括在线最近邻图的中心极限定理，其有效性在(Wade, 2009; Penrose和Wade, 2009)中被猜想。 我们还将这些技术应用于推导Gilbert图、$k$-最近邻图和径向生成树的边泛函的定量中心极限定理，在已知和未知定性中心极限定理的情况下都进行了研究。 显示英文摘要

摘要： We establish new explicit bounds on the Gaussian approximation of Poisson functionals based on novel estimates of moments of Skorohod integrals. Combining these with the Malliavin-Stein method, we derive bounds in the Wasserstein and Kolmogorov distances whose application requires minimal moment assumptions on add-one cost operators $\unicode{x2014}$ thereby extending the results from (Last, Peccati and Schulte, 2016). Our applications include a CLT for the Online Nearest Neighbour graph, whose validity was conjectured in (Wade, 2009; Penrose and Wade, 2009). We also apply our techniques to derive quantitative CLTs for edge functionals of the Gilbert graph, of the $k$-Nearest Neighbour graph and of the Radial Spanning Tree, both in cases where qualitative CLTs are known and unknown.