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A Gaussian ensemble of Hermitian matrices with an arbitrary ratio of their symmetric and anti-symmetric parts is studied. Similarly a Gaussian ensemble of Hermitian quaternion matrices with an arbitrary ratio of their self-dual and anti-self-dual parts is studied. Analytical expressions for the correlation and cluster functions as well as their limits when the order of the matrices is large, are derived for both ensembles.
Mehta et al. (Sun,) studied this question.
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