Quantitative CLTs on the Poisson space via Skorohod estimates and $p$-Poincar\'e inequalities

Tara Trauthwein

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arXiv · 2212.03782

Quantitative CLTs on the Poisson space via Skorohod estimates and $p$-Poincar\'e inequalities

Tara Trauthwein

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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 $\unicode{x2014}$ 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.

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Tara Trauthwein. 2022-12-07. Quantitative CLTs on the Poisson space via Skorohod estimates and $p$-Poincar\'e inequalities. https://arxiv.org/abs/2212.03782

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