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Combining analytical and numerical methods, we investigate properties of the two-body random ensemble (TBRE). We compare the TBRE with the Gaussian orthogonal ensemble of random matrices. Using the geometric properties of the nuclear shell model, we discuss the information content of nuclear spectra, and gain insight in the difficulties encountered when fitting the effective interaction. We exhibit the existence of correlations between spectral widths pertaining to different quantum numbers.doi:10.1142/s0218301306005435 fatcat:3cljizfivrdmbm7uu4min4zmkm