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The Correlated Jacobi and the Correlated Cauchy–Lorentz Ensembles
Wirtz T., Waltner D., Kieburg M.,
Published in Springer New York LLC
Volume: 162
Issue: 2
Pages: 495 - 521
We calculate the k-point generating function of the correlated Jacobi ensemble using supersymmetric methods. We use the result for complex matrices for k=1 to derive a closed-form expression for the eigenvalue density. For real matrices we obtain the density in terms of a twofold integral that we evaluate numerically. For both expressions we find agreement when comparing with Monte Carlo simulations. Relations between these quantities for the Jacobi and the Cauchy–Lorentz ensemble are derived. © 2015, Springer Science+Business Media New York.
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Published in Springer New York LLC
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