On the rate of convergence and Berry-Esseen type theorems for a multivariate free central limit theorem

2007/12/18 by Roland Speicher, Speicher, Roland · 2 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Operator Algebras (math.OA) #Random Matrices and Applications #Stochastic processes and statistical mechanics #math.OA

paper · pdf · doi:10.48550/arxiv.0712.2974

14 pages

arxiv created 2007/12/18 · openalex publication_date 2007/12/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We address the question of a Berry Esseen type theorem for the speed of convergence in a multivariate free central limit theorem. For this, we estimate the difference between the operator-valued Cauchy transforms of the normalized partial sums in an operator-valued free central limit theorem and the Cauchy transform of the limiting operator-valued semicircular element.

Cited by

• Free Stein kernels and an improvement of the free logarithmic Sobolev\n inequality
• Rates of convergence in the Free Multiplicative Central Limit Theorem

Related

• Operator-valued and multivariate free Berry-Esseen theorems
• Berry-Esseen bounds for the multivariate B-free CLT and operator-valued matrices
• Rates of convergence in the free central limit theorem
• Berry-Esseen bounds for the chi-square distance in the Central Limit Theorem: a Markovian approach
• Rates of convergence in the Free Multiplicative Central Limit Theorem