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Completing the picture for the smallest eigenvalue of real Wishart matrices
G. Akemann, T. Guhr, M. Kieburg +2
Rectangular real matrices with a Gaussian distribution appear very frequently in data analysis, condensed matter physics and quantum field theory. A central…
Universal distribution of Lyapunov exponents for products of Ginibre matrices
Gernot Akemann, Zdzislaw Burda, Mario Kieburg
Starting from exact analytical results on singular values and complex eigenvalues of products of independent Gaussian complex random matrices also called Ginibre ensemb…
Permanental processes from products of complex and quaternionic induced Ginibre ensembles
G. Akemann, J. R. Ipsen, E. Strahov
We consider products of independent random matrices taken from the induced Ginibre ensemble with complex or quaternion elements. The joint densities for the complex eigenvalues of…
A singular-potential random matrix model arising in mean-field glassy systems
Gernot Akemann, Dario Villamaina, Pierpaolo Vivo
We consider an invariant random matrix model where the standard Gaussian potential is distorted by an additional single pole of order . We compute the average or macroscopic spe…