1202.3925 (Sebastian Schierenberg et al.)

Wigner surmise for mixed symmetry classes in random matrix theory    [PDF]

Sebastian Schierenberg, Falk Bruckmann, Tilo Wettig

We consider the nearest-neighbor spacing distributions of mixed random matrix
ensembles interpolating between different symmetry classes, or between
integrable and non-integrable systems. We derive analytical formulas for the
spacing distributions of 2x2 or 4x4 matrices and show numerically that they
provide very good approximations for those of random matrices with large
dimension. This generalizes the Wigner surmise, which is valid for pure
ensembles that are recovered as limits of the mixed ensembles. We show how the
coupling parameters of small and large matrices must be matched depending on
the local eigenvalue density.

View original: http://arxiv.org/abs/1202.3925