191 citations · 607 across the 22 of their papers we have counts for
17 papers · 1 filter
The Laguerre Unitary Process
J. R. Ipsen
We define a new matrix-valued stochastic process with independent stationary increments from the Laguerre Unitary Ensemble, which in a certain sense may be considered a matrix gene…
A generalisation of the relation between zeros of the complex Kac polynomial and eigenvalues of truncated unitary matrices
Peter J. Forrester, Jesper R. Ipsen
The zeros of the random Laurent series , where each is an independent standard complex Gaussian, is known to correspond to the scaled eigenval…
Kac-Rice fixed point analysis for single- and multi-layered complex systems
J. R. Ipsen, P. J. Forrester
We present a null model for single- and multi-layered complex systems constructed using homogeneous and isotropic random Gaussian maps. By means of a Kac-Rice formalism, we show th…
Orthogonal and symplectic Harish-Chandra integrals and matrix product ensembles
Peter J. Forrester, Jesper R. Ipsen, Dang-Zheng Liu +1
In this paper, we highlight the role played by orthogonal and symplectic Harish-Chandra integrals in the study of real-valued matrix product ensembles. By making use of these integ…
How many eigenvalues of a product of truncated orthogonal matrices are real?
P. J. Forrester, J. R. Ipsen, S. Kumar
A truncation of a Haar distributed orthogonal random matrix gives rise to a matrix whose eigenvalues are either real or complex conjugate pairs, and are supported within the closed…
May-Wigner transition in large random dynamical systems
J. R. Ipsen
We consider stability in a class of random non-linear dynamical systems characterised by a relaxation rate together with a Gaussian random vector field which is white-in-time and s…
Matrix product ensembles of Hermite-type and the hyperbolic Harish-Chandra-Itzykson-Zuber integral
P. J. Forrester, J. R. Ipsen, Dang-Zheng Liu
We investigate spectral properties of a Hermitised random matrix product which, contrary to previous product ensembles, allows for eigenvalues on the full real line. We prove that…
Selberg integral theory and Muttalib--Borodin ensembles
P. J. Forrester, J. R. Ipsen
We study Muttalib--Borodin ensembles --- particular eigenvalue PDFs on the half-line --- with classical weights, i.e. Laguerre, Jacobi or Jacobi prime. We show how the theory of th…
Real eigenvalue statistics for products of asymmetric real Gaussian matrices
P. J. Forrester, J. R. Ipsen
Random matrices formed from i.i.d. standard real Gaussian entries have the feature that the expected number of real eigenvalues is non-zero. This property persists for products of…
Isotropic Brownian motions over complex fields as a solvable model for May-Wigner stability analysis
J. R. Ipsen, H. Schomerus
We consider matrix-valued stochastic processes known as isotropic Brownian motions, and show that these can be solved exactly over complex fields. While these processes appear in a…
Products of Independent Gaussian Random Matrices
J. R. Ipsen
This thesis reviews recent progress on products of random matrices from the perspective of exactly solved Gaussian random matrix models. We derive exact formulae for the correlatio…
Recent exact and asymptotic results for products of independent random matrices
Gernot Akemann, Jesper R. Ipsen
In this review we summarise recent results for the complex eigenvalues and singular values of finite products of finite size random matrices, their correlation functions and asympt…
Lyapunov exponents for products of rectangular real, complex and quaternionic Ginibre matrices
J. R. Ipsen
We study the joint density of eigenvalues for products of independent rectangular real, complex and quaternionic Ginibre matrices. In the limit where the number of matrices tends t…
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…
Weak Commutation Relations and Eigenvalue Statistics for Products of Rectangular Random Matrices
J. R. Ipsen, M. Kieburg
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 distribu…
Products of Rectangular Random Matrices: Singular Values and Progressive Scattering
Gernot Akemann, Jesper R. Ipsen, Mario Kieburg
We discuss the product of rectangular random matrices with independent Gaussian entries, which have several applications including wireless telecommunication and econophysics.…
Products of Independent Quaternion Ginibre Matrices and their Correlation Functions
J. R. Ipsen
We discuss the product of independent induced quaternion () Ginibre matrices, and the eigenvalue correlations of this product matrix. The joint probability density function fo…