Optimal Berry-Esseen bounds on the Poisson space
Ehsan Azmoodeh, Giovanni Peccati
TL;DR
This paper develops new lower bounds for normal approximation of Poisson functionals, extending previous Gaussian-based results, with applications to edge counting in random geometric graphs.
Contribution
It introduces optimal Berry-Esseen bounds on the Poisson space, generalizing prior Gaussian space results to Poisson functionals.
Findings
New lower bounds for Wasserstein distance in Poisson space
Extension of Gaussian space results to Poisson functionals
Application to edge counting in random geometric graphs
Abstract
We establish new lower bounds for the normal approximation in the Wasserstein distance of random variables that are functionals of a Poisson measure. Our results generalize previous findings by Nourdin and Peccati (2012, 2015) and Bierm\'e, Bonami, Nourdin and Peccati (2013), involving random variables living on a Gaussian space. Applications are given to optimal Berry-Esseen bounds for edge counting in random geometric graphs.
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Taxonomy
TopicsPoint processes and geometric inequalities · Heavy Metal Exposure and Toxicity · Geometric Analysis and Curvature Flows