Disordered ensembles of random matrices

O. Bohigas 1, J. X. de Carvalho 2, 3, M. P. Pato 1, 2

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 77 (2008) 011122

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.

  • 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 2. Instituto de Fisica,
    Universidade de São Paulo
  • 3. Max-Planck-Institut für Physik komplexer Systeme,