Level Repulsion in Constrained Gaussian Random-Matrix Ensembles

Abstract

Introducing sets of constraints, we define new classes of random-matrix ensembles, the constrained Gaussian unitary (CGUE) and the deformed Gaussian unitary (DGUE) ensembles. The latter interpolate between the GUE and the CGUE. We derive a sufficient condition for GUE-type level repulsion to persist in the presence of constraints. For special classes of constraints, we extend this approach to the orthogonal and to the symplectic ensembles. A generalized Fourier theorem relates the spectral properties of the constraining ensembles with those of the constrained ones. We find that in the DGUEs, level repulsion always prevails at a sufficiently short distance and may be lifted only in the limit of strictly enforced constraints.

20 pages, no figures. New section added

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Cited by in corpus (3)

• Random Matrices and Chaos in Nuclear Physics
• Recursion for the smallest eigenvalue density of $\beta$-Wishart-Laguerre ensemble
• Spectral fluctuation properties of constrained unitary ensembles of Gaussian-distributed random matrices