Operator-valued and multivariate free Berry-Esseen theorems

2012/02/13 by Tobias Mai, Roland Speicher, Mai, Tobias +1 · 1 citation
Mathematics · #FOS: Mathematics #Mathematical functions and polynomials #Operator Algebras (math.OA) #Random Matrices and Applications #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1202.2740

openalex publication_date 2012/02/13 · 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. Since we have to deal with in general non-self-adjoint operators, we introduce the notion of matrix-valued resolvent sets and study the behavior of Cauchy transforms on them.

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• Operator-Valued Matrices with Free or Exchangeable Entries

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