Spectrum of subblocks of structured random matrices : A free probability approach
Résumé
We present a new efficient method, based on an extremization problem, for computing the spectrum of subblocks of large structured random matrices. This method applies to ensembles of matrices satisfying three fundamental properties, which we discuss. We present different proofs - combinatorial or algebraic - of the validity of this method, which all have some connection with free probability. We illustrate this method with well known examples of unstructured matrices, including Haar randomly rotated matrices, as well as with the example of structured random matrices arising in the quantum symmetric simple exclusion process.