Ensemble of Random Matrices with a Random Bias

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Abstract
The ensemble exp [−γ Tr (H − H0)2], where the eigenvalues λn of H0 are given by some distribution f(λ), is investigated. In particular, the limits of large and small γ for the orthogonal case are considered. Formal expressions are obtained for various distributions of the eigenvalues in the two limits. The approximation developed in the large‐γ limit is also applied to the thermodynamics of an incompletely specified system. Further, it is shown that this approximation is easily extended to include the unitary and symplectic ensembles.

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