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- Gernot Akemann, Jesper R Ipsen, Mario Kieburg
- Physical review. E, Statistical, nonlinear, and…
- 2013

We discuss the product of M rectangular random matrices with independent Gaussian entries, which have several applications, including wireless telecommunication and econophysics. For complex matrices an explicit expression for the joint probability density function is obtained using the Harish-Chandra-Itzykson-Zuber integration formula. Explicit expressions… (More)

- Jesper R Ipsen, Mario Kieburg
- Physical review. E, Statistical, nonlinear, and…
- 2014

We study the joint probability density of the eigenvalues of a product of rectangular real, complex, or quaternion random matrices in a unified way. The random matrices are distributed according to arbitrary probability densities, whose only restriction is the invariance under left and right multiplication by orthogonal, unitary, or unitary symplectic… (More)

- Gernot Akemann, Mario Kieburg, Lu Wei
- ArXiv
- 2013

We consider the product of M quadratic random matrices with complex elements and no further symmetry, where all matrix elements of each factor have a Gaussian distribution. This generalises the classical Wishart-Laguerre Gaussian Unitary Ensemble with M = 1. In this paper we first compute the joint probability distribution for the singular values of the… (More)

- Christian Recher, Mario Kieburg, Thomas Guhr
- Physical review letters
- 2010

Wishart correlation matrices are the standard model for the statistical analysis of time series. The ensemble averaged eigenvalue density is of considerable practical and theoretical interest. For complex time series and correlation matrices, the eigenvalue density is known exactly. In the real case, a fundamental mathematical obstacle made it forbiddingly… (More)

- Mario Kieburg, Jacobus J M Verbaarschot, Savvas Zafeiropoulos
- Physical review letters
- 2012

We find the lattice spacing dependence of the eigenvalue density of the non-Hermitian Wilson Dirac operator in the ϵ domain. The starting point is the joint probability density of the corresponding random matrix theory. In addition to the density of the complex eigenvalues we also obtain the density of the real eigenvalues separately for positive and… (More)

We study integration over functions on superspaces. These functions are invariant under a transformation which maps the whole superspace onto the part of the superspace which only comprises purely commuting variables. We get a compact expression for the differential operator with respect to the commuting variables which results from Berezin integration over… (More)

Recently, two different approaches were put forward to extend the supersymmetry method in random matrix theory from Gaussian ensembles to general rotation invariant ensembles. These approaches are the generalized Hubbard– Stratonovich transformation and the superbosonization formula. Here, we prove the equivalence of both approaches. To this end, we reduce… (More)

Recently, the supersymmetry method was extended from Gaussian ensembles to arbitrary unitarily invariant matrix ensembles by generalizing the Hubbard–Stratonovich transformation. Here, we complete this extension by including arbitrary orthogonally and unitary–symplectically invariant matrix ensembles. The results are equivalent to, but the approach is… (More)

We study discretization effects of the Wilson and staggered Dirac operator with N c > 2 using chi-ral random matrix theory (chRMT). We obtain analytical results for the joint probability density of Wilson-chRMT in terms of a determinantal expression over complex pairs of eigenvalues, and real eigenvalues corresponding to eigenvectors of positive or negative… (More)

We analyze Dirac spectra of two-dimensional QCD like theories both in the continuum and on the lattice and classify them according to random matrix theories sharing the same global symmetries. The classification is di↵erent from QCD in four dimensions because the anti-unitary symmetries do not commute with 5. Therefore in a chiral basis, the number of… (More)