Abstract
Exact distributions are given for the two-dimensional case when the mean of the off-diagonal element is non-zero. The joint eigenvalue distribution for theN dimensional case, derived using the volume element in the space ofN ×N orthogonal matrices, is checked by rederiving the exact results forN=2. The smooth nature of theN-dimensional joint distribution supports the claim of the method of moments that the single eigenvalue distribution is a smooth function of the ratio of mean-to-mean square deviation.
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Ullah, N. On the joint eigenvalue distribution for the matrix ensembles with non zero mean. Pramana - J Phys 15, 45–51 (1980). https://doi.org/10.1007/BF02847909
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DOI: https://doi.org/10.1007/BF02847909