Hyperbolic disordered ensembles of random matrices

Details Hyperbolic disordered ensembles of random matrices Hyperbolic disordered ensembles of random matrices

2011-10-11

arxiv.org/abs/1110.2443v1

Phys. Rev E 84, 031121 (2011)

Physics

Condensed Matter

Disordered Systems and Neural Networks

14 pages, 6 figures

Scientific paper

10.1103/PhysRev.84.031121

Using the simple procedure, recently introduced, of dividing Gaussian matrices by a positive random variable, a family of random matrices is generated characterized by a behavior ruled by the generalized hyperbolic distribution. The spectral density evolves from the semi-circle law to a Gaussian-like behavior while concomitantly the local fluctuations show a transition from the Wigner-Dyson to the Poisson statistics. Long range statistics such as number variance exhibit large fluctuations typical of non-ergodic ensembles.

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