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Pré-Publication, Document De Travail Année : 2018

Operator-Valued Matrices with Free or Exchangeable Entries

Résumé

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.

Dates et versions

hal-01961841 , version 1 (20-12-2018)

Identifiants

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Marwa Banna, Guillaume Cébron. Operator-Valued Matrices with Free or Exchangeable Entries. 2018. ⟨hal-01961841⟩
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