Quantitative CLTs on the Poisson space via Skorohod estimates and $p$-Poincar\'e inequalities
Abstract
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 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 -Nearest Neighbour graph and of the Radial Spanning Tree, both in cases where qualitative CLTs are known and unknown.
Keywords
Cite
@article{arxiv.2212.03782,
title = {Quantitative CLTs on the Poisson space via Skorohod estimates and $p$-Poincar\'e inequalities},
author = {Tara Trauthwein},
journal= {arXiv preprint arXiv:2212.03782},
year = {2022}
}