Sparse block-structured random matrices: universality

Abstract

We study ensembles of sparse random block matrices generated from the adjacency matrix of a Erdös-Renyi random graph with N vertices of average degreeentry. Z, inserting a real symmetric d × d random block at each non-vanishing

The spectral boundary of block structured random matrices

“…This ensemble is a generalisation of the one studied in [9], which is itself a generalisation of the ensemble introduced in the seminal paper [22]. Note that block structured random matrix ensembles have been studied from the mathematical perspective [23][24][25][26][27] and from the physics perspective [28][29][30][31], since models with M internal degrees of freedom can be useful to understand low energy vibrational modes in glasses.…”