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 ErdösRenyi 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.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 April 2022
 DOI:
 10.1088/17518121/ac3468
 arXiv:
 arXiv:2106.10125
 Bibcode:
 2022JPhA...55q5202C
 Keywords:

 sparse;
 random;
 block;
 random matrices;
 sparse matrices;
 Mathematical Physics;
 Condensed Matter  Statistical Mechanics;
 Mathematics  Combinatorics;
 Mathematics  Probability
 EPrint:
 31 pages