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arXiv · 1811.05373

Operator-Valued Matrices with Free or Exchangeable Entries

Marwa Banna·Guillaume Cébron
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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 prove quantitative convergence to operator-valued semicircular elements over some subalgebra in terms of Cauchy transforms. As direct applications, we obtain explicit rates of convergence for a large class of random block matrices with independent or correlated blocks. Our approach relies on a noncommutative extension of the Lindeberg method and operator-valued Gaussian interpolation techniques.

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Marwa Banna, Guillaume Cébron. 2018-11-13. Operator-Valued Matrices with Free or Exchangeable Entries. https://arxiv.org/abs/1811.05373

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