Non-Hermitian β-ensemble with real eigenvalues

O. Bohigas 1 and M. P. Pato 2

AIP ADVANCES 3, 032130 (2013)

By removing the Hermitian condition of the so-called β-ensemble of tridiagonal matrices, an ensemble of non-Hermitian random matrices is constructed whose eigenvalues are all real. It is shown that they belong to the class of pseudo-Hermitian operators. Its statistical properties are investigated.

  • 1 CNRS, Universite Paris-Sud, UMR8626, LPTMS, Orsay Cedex, F-91405, France
  • 2 Instıtuto de F ́ısica, Universidade de S ̃ao Paulo, Caixa Postal 66318, 05314-970 Sao Paulo, S.P., Brazil