Quantitative central limit theorems for Mexican needlet coefficients on circular Poisson fields

TL;DR

This paper establishes quantitative central limit theorems for Mexican needlet coefficients on circular Poisson fields, providing explicit convergence rates to Gaussianity using Stein-Malliavin methods.

Contribution

It introduces new quantitative CLTs for Mexican needlet coefficients on the circle, leveraging Stein-Malliavin techniques and concentration properties.

Findings

Explicit convergence rates to Gaussianity for Mexican needlet coefficients

Application of Stein-Malliavin techniques to circular Poisson fields

Enhanced understanding of wavelet coefficient behavior on circular domains

Abstract

The aim of this paper is to establish rates of convergence to Gaussianity for wavelet coefficients on circular Poisson random fields. This result is established by using the Stein-Malliavin techniques introduced by Peccati and Zheng (2011) and the concentration properties of so-called Mexican needlets on the circle