On a Berry-Esseen type limit theorem for Boolean convolution
Mauricio Salazar
TL;DR
This paper establishes a precise rate of convergence in the Boolean central limit theorem for measures with finite sixth moments, using a quantitative inversion formula as the main tool.
Contribution
It provides a sharp estimate of convergence speed in the Boolean CLT, advancing understanding of non-commutative probability limits.
Findings
Derived a sharp convergence rate for Boolean CLT
Utilized a quantitative Stieltjes-Perron inversion formula
Applicable to measures with finite sixth moments
Abstract
We obtain a sharp estimate of the speed of convergence in the Boolean central limit theorem for measures of finite sixth moment. The main tool is a quantitative version of the Stieltjes-Perron inversion formula.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Random Matrices and Applications · Spectral Theory in Mathematical Physics