Disordered ensembles of random matrices

TL;DR

This paper introduces a simple method to generate disordered matrix ensembles and random graph models that interpolate between classical and scale-free networks, revealing nonergodic properties.

Contribution

It presents a novel procedure of dividing Gaussian matrices by a random variable to create orthogonal invariant stable Lévy ensembles and explores their nonergodic behavior.

Findings

Generated ensembles exhibit nonergodicity.

Method interpolates between Erdős-Rényi and scale-free models.

Provides insight into disordered systems and network structures.

Abstract

It is shown that the families of generalized matrix ensembles recently considered which give rise to an orthogonal invariant stable L\'{e}vy ensemble can be generated by the simple procedure of dividing Gaussian matrices by a random variable. The nonergodicity of this kind of disordered ensembles is investigated. It is shown that the same procedure applied to random graphs gives rise to a family that interpolates between the Erd\"{o}s-Renyi and the scale free models.