2 citations · 3 across the 4 of their papers we have counts for
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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…