Sparse Random Block Matrices
Abstract
The spectral moments of ensembles of sparse random block matrices are analytically evaluated in the limit of large order. The structure of the sparse matrix corresponds to the Erd\"os-Renyi random graph. The blocks are i.i.d. random matrices of the classical ensembles GOE or GUE. The moments are evaluated for finite or infinite dimension of the blocks. The correspondences between sets of closed walks on trees and classes of irreducible partitions studied in free probability together with functional relations are powerful tools for analytic evaluation of the limiting moments. They are helpful to identify probability laws for the blocks and limits of the parameters which allow the evaluation of all the spectral moments and of the spectral density.
Cite
@article{arxiv.2106.10125,
title = {Sparse Random Block Matrices},
author = {Giovanni M. Cicuta and Mario Pernici},
journal= {arXiv preprint arXiv:2106.10125},
year = {2022}
}
Comments
31 pages