Jesper Ipsen

Nonlinearity-generated resilience in large complex systems

S Belga Fedeli, Y Fyodorov, JR Ipsen

Journal article  |  2021  |  PHYSICAL REVIEW E

We consider a generic nonlinear extension of May's 1972 model by including all higher-order terms in the expansion around the chos..

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

PJ Forrester, JR Ipsen, S Kumar

Journal article  |  2020  |  EXPERIMENTAL MATHEMATICS

A truncation of a Haar distributed orthogonal random matrix gives rise to a matrix whose eigenvalues are either real or complex co..

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

The zeros of the random Laurent series 1/μ-∑j=1∞cj/zj, where each cj is an independent standard complex Gaussian, is known to corr..

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

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

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

We present a null model for single- and multi-layered complex systems constructed using homogeneous and isotropic random Gaussian ..

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 POINCARE

We investigate spectral properties of a Hermitised random matrix product which, contrary to previous product ensembles, allows for..

Selberg integral theory and Muttalib-Borodin ensembles

PJ Forrester, JR Ipsen

Journal article  |  2018  |  ADVANCES IN APPLIED MATHEMATICS

We study Muttalib–Borodin ensembles — particular eigenvalue PDFs on the half-line — with classical weights, i.e. Laguerre, Jacobi ..

May-Wigner transition in large random dynamical systems

JR Ipsen

Journal article  |  2017  |  JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT

We consider stability in a class of random non-linear dynamical systems characterised by a relaxation rate together with a Gaussia..