Jesper Ipsen

Consequences of Dale's law on the stability-complexity relationship of random neural networks

JR Ipsen, ADH Peterson

Journal article  |  2020  |  Physical Review E

In the study of randomly connected neural network dynamics there is a phase transition from a simple state with few equilibria to ..

A generalisation of the relation between zeros of the complex Kac polynomial and eigenvalues of truncated unitary matrices

Peter J Forrester, Jesper R Ipsen

Journal article  |  2019  |  Probability Theory and Related Fields

Orthogonal and symplectic Harish-Chandra integrals and matrix product ensembles

Peter J Forrester, Jesper R Ipsen, Dang-Zheng Liu, Lun Zhang

Journal article  |  2019  |  Random Matrices: Theory and Applications

In this paper, we highlight the role played by orthogonal and symplectic Harish-Chandra integrals in the study of real-valued matr..

Multiplicative convolution of real asymmetric and real anti-symmetric matrices

Mario Kieburg, Peter J Forrester, Jesper R Ipsen

Journal article  |  2019  |  Advances in Pure and Applied Mathematics

Abstract The singular values of products of standard complex Gaussian random matrices, or sub-blocks of Haar distribut..

Kac-Rice fixed point analysis for single- and multi-layered complex systems

JR Ipsen, PJ Forrester

Journal article  |  2018  |  Journal of Physics A: Mathematical and Theoretical

How Many Eigenvalues of a Product of Truncated Orthogonal Matrices are Real?

PJ Forrester, JR Ipsen, S Kumar

Journal article  |  2018  |  Experimental Mathematics

Matrix Product Ensembles of Hermite Type and the Hyperbolic Harish-Chandra-Itzykson-Zuber Integral

PJ Forrester, JR Ipsen, Dang-Zheng Liu

Journal article  |  2018  |  Annales Henri Poincaré

Selberg integral theory and Muttalib-Borodin ensembles

PJ Forrester, JR Ipsen

Journal article  |  2018  |  Advances in Applied Mathematics

May-Wigner transition in large random dynamical systems

JR Ipsen

Journal article  |  2017  |  Journal of Statistical Mechanics: Theory and Experiment

Real eigenvalue statistics for products of asymmetric real Gaussian matrices

Peter J Forrester, Jesper R Ipsen

Journal article  |  2016  |  Linear Algebra and its Applications

Isotropic Brownian motions over complex fields as a solvable model for May-Wigner stability analysis

JR Ipsen, H Schomerus

Journal article  |  2016  |  Journal of Physics A: Mathematical and Theoretical

RECENT EXACT AND ASYMPTOTIC RESULTS FOR PRODUCTS OF INDEPENDENT RANDOM MATRICES

Gernot Akemann, Jesper R Ipsen

Journal article  |  2015  |  Acta Physica Polonica B

Lyapunov exponents for products of rectangular real, complex and quaternionic Ginibre matrices

JR Ipsen

Journal article  |  2015  |  J. Phys. A

Permanental processes from products of complex and quaternionic induced Ginibre ensembles

Gernot Akemann, Jesper R Ipsen, Eugene Strahov

Journal article  |  2014  |  Random Matrices: Theory and Applications

Weak commutation relations and eigenvalue statistics for products of rectangular random matrices

Jesper R Ipsen, Mario Kieburg

Journal article  |  2014  |  Phys. Rev. E

Products of rectangular random matrices: Singular values and progressive scattering

Gernot Akemann, Jesper R Ipsen, Mario Kieburg

Journal article  |  2013  |  PHYSICAL REVIEW E

Products of independent quaternion Ginibre matrices and their correlation functions

JR Ipsen

Journal article  |  2013  |  J. Phys. A: Math. Theor.

Baryon number Dirac spectrum in QCD

JR Ipsen, K Splittorff

Journal article  |  2012  |  Physical Review D

Products of Independent Gaussian Random Matrices

JR Ipsen

Journal article

This thesis reviews recent progress on products of random matrices from the perspective of exactly solved Gaussian random matrix m..