Bohigas O, Pato MP. Hyperbolic disordered ensembles of random matrices.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011;
84:031121. [PMID:
22060342 DOI:
10.1103/physreve.84.031121]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2011] [Revised: 08/01/2011] [Indexed: 05/31/2023]
Abstract
Using the recently introduced simple procedure 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 semicircle 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 nonergodic ensembles.
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