# Operator-Valued Matrices with Free or Exchangeable Entries

Abstract : We study matrices whose entries are free or exchangeable noncommutative elements in some tracial $W^*$-probability space. More precisely, we consider operator-valued Wigner and Wishart matrices and give for the associated Cauchy transforms explicit rates of convergence to operator-valued semicircular elements over some subalgebra. Applications to block random matrices with a Wigner or circulant structure and in independent or correlated blocks are also given. Our approach relies on a noncommutative extension of the Lindeberg method and Gaussian interpolation techniques.
Type de document :
Pré-publication, Document de travail
33 pages. 2018
Domaine :
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https://hal.archives-ouvertes.fr/hal-01961841
Contributeur : Guillaume Cébron <>
Soumis le : jeudi 20 décembre 2018 - 11:21:45
Dernière modification le : vendredi 21 décembre 2018 - 10:19:42

### Identifiants

• HAL Id : hal-01961841, version 1
• ARXIV : 1811.05373

### Citation

Marwa Banna, Guillaume Cébron. Operator-Valued Matrices with Free or Exchangeable Entries. 33 pages. 2018. 〈hal-01961841〉

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