Operator-valued matrices with free or exchangeable entries

Marwa Banna, Guillaume Cébron

Research output: Contribution to journalArticlepeer-review


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 and the Kolmogorov distance. 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.

Original languageEnglish (US)
Pages (from-to)503-537
Number of pages35
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Issue number1
StatePublished - Feb 2023


  • Matrices with free entries
  • Matrices with noncommutative exchangeable entries
  • Noncommutative Lindeberg method
  • Operator-valued free probability
  • Random block matrices
  • Random operators

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Operator-valued matrices with free or exchangeable entries'. Together they form a unique fingerprint.

Cite this