Spectral fluctuation properties of constrained unitary ensembles of Gaussian-distributed random matrices

Details Spectral fluctuation properties of constrained unitary ensembles of Gaussian-distributed random matrices Spectral fluctuation properties of constrained unitary ensembles of Gaussian-distributed random matrices

2009-01-28

arxiv.org/abs/0901.4389v1

J. Phys. A: Math. Theor. 42 (2009) 155203

Physics

Mathematical Physics

15 pages

Scientific paper

10.1088/1751-8113/42/15/155203

We investigate the spectral fluctuation properties of constrained ensembles of random matrices (defined by the condition that a number N(Q) of matrix elements vanish identically; that condition is imposed in unitarily invariant form) in the limit of large matrix dimension. We show that as long as N(Q) is smaller than a critical value (at which the quadratic level repulsion of the Gaussian unitary ensemble of random matrices may be destroyed) all spectral fluctuation measures have the same form as for the Gaussian unitary ensemble.

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