2018/11/13 by Marwa Banna, Banna, Marwa, Guillaume Cébron +1
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Operator Algebras (math.OA) #Probability (math.PR) #Random Matrices and Applications
paper · doi:10.48550/arxiv.1811.05373
openalex publication_date 2018/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.