# The correlated Jacobi and the correlated Cauchy-Lorentz ensembles

Wirtz T, Waltner D, Kieburg M, Kumar S (2016)
Journal of Statistical Physics 162(2): 495-521.

Journal Article | Published | English

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We calculate the k-point generating function of the correlated Jacobi ensemble using supersymmetric methods. We use the result for complex matrices for 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.
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Wirtz T, Waltner D, Kieburg M, Kumar S. The correlated Jacobi and the correlated Cauchy-Lorentz ensembles. Journal of Statistical Physics. 2016;162(2):495-521.
Wirtz, T., Waltner, D., Kieburg, M., & Kumar, S. (2016). The correlated Jacobi and the correlated Cauchy-Lorentz ensembles. Journal of Statistical Physics, 162(2), 495-521.
Wirtz, T., Waltner, D., Kieburg, M., and Kumar, S. (2016). The correlated Jacobi and the correlated Cauchy-Lorentz ensembles. Journal of Statistical Physics 162, 495-521.
Wirtz, T., et al., 2016. The correlated Jacobi and the correlated Cauchy-Lorentz ensembles. Journal of Statistical Physics, 162(2), p 495-521.
T. Wirtz, et al., “The correlated Jacobi and the correlated Cauchy-Lorentz ensembles”, Journal of Statistical Physics, vol. 162, 2016, pp. 495-521.
Wirtz, T., Waltner, D., Kieburg, M., Kumar, S.: The correlated Jacobi and the correlated Cauchy-Lorentz ensembles. Journal of Statistical Physics. 162, 495-521 (2016).
Wirtz, Tim, Waltner, Daniel, Kieburg, Mario, and Kumar, Santosh. “The correlated Jacobi and the correlated Cauchy-Lorentz ensembles”. Journal of Statistical Physics 162.2 (2016): 495-521.
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