Functional second-order Gaussian Poincar\'e inequalities

Anna Vidotto; Guangqu Zheng

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arXiv · 2506.13571

Functional second-order Gaussian Poincar\'e inequalities

Anna Vidotto·Guangqu Zheng

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Abstract

In this paper, we work in the framework of Hilbert-valued Wiener structures and derive a functional version of the second-order Gaussian Poincar\'e inequality that leads to abstract bounds for Gaussian process approximation in $d_2$ distance. Our abstract bounds are flexible and can be applied in various examples including functional Breuer-Major central limit theorems, shallow neural networks, and spatial statistics of SPDEs solutions.

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Anna Vidotto, Guangqu Zheng. 2025-06-16. Functional second-order Gaussian Poincar\'e inequalities. https://arxiv.org/abs/2506.13571

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