The correlated Jacobi and the correlated Cauchy-Lorentz ensembles
Wirtz, Tim
Wirtz
Tim
Waltner, Daniel
Waltner
Daniel
Kieburg, Mario
Kieburg
Mario
Kumar, Santosh
Kumar
Santosh
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.
162
2
495-521
495-521
Springer
2016