I’m a mathematical physicist and coffee addict. I’m interested in understanding complex phenomena through simple models using my favourite tool, Random Matrix Theory. I am based at the University of Melbourne and I spent most of my spare time making my kids laugh.

Currently, I am a DECRA fellow funded by the Australian Research Council. I am recuiting a PhD student for this project.

For a full list of my publications, see the links below.

Stability and Complexity: New insights from Random Matrix Theory.

Complexity is a rule of nature: large ecosystems, the human brain, and turbulent fluids are merely a few examples of complex systems. This project aims to study and classify criteria of stability in large complex systems based on universal probabilistic models. This project expects to generate new important understanding of stability using cutting-edge techniques from random matrix theory. Expected outcomes of this project include development and expansion of an innovative mathematical framework and techniques which allow a unified and universal approach to the question of stability in large complex systems.

This project is funded by the Australian Research Council. I am currently recuiting a PhD student for this project. Please contact me if you are interested.

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

, Probab. Theor. Rel. Fields 175 (2019) 833 , arXiv:1807.06743 - Multiplicative convolution of real asymmetric and real antisymmetric
matrices

, Adv. Pure Appl. Math. 10 (2019) 467, arXiv:1712.04916 - Orthogonal and symplectic Harish-Chandra integrals and matrix product
ensembles

, Random Matrices Theor. Appl. 08 (2019) 1950015, arXiv:1711.10691 - Kac-Rice fixed point analysis for single-and multi-layered complex
systems

, Random J. Phys. A 51 (2018) 474003, arXiv:1807.05790

Invited contribution to Special Issue: Random Matrices, the first 90 years - How many eigenvalues of a product of truncated orthogonal matrices are
real?

, Experiment. Math. (2018) 1, arXiv:1708.00967 - Matrix Product ensembles of Hermite-type and the hyperbolic
Harish-Chandra–Itzykson–Zuber integral

, Ann. Henri Poincaré 19 (2018) 1307, arXiv:1702.07100 - Selberg integral theory and Muttalib-Borodin ensembles

, Adv. Appl. Math. 95 (2018) 152, arXiv:1612.06517 - May–Wigner transition in large random dynamical systems

, J. Stat. Mech. (2017) 093209, arXiv:1705.05047 - Real eigenvalue statistics for products of asymmetric real Gaussian
matrices

, Lin. Alg. Appl. 510 259 (2016), arXiv:1608.04097 - Isotropic Brownian motion over complex fields as a solvable model for May–Wigner
stability analysis

, J. Phys. A 49 385201 (2016), arXiv:1602.06364 - Lyapunov exponents for products of rectangular real,complex & quaternionic
Ginibre matrices

, J. J. Phys. A 48, 155204 (2015), arXiv:1412.3003 Publisher's pick - Permanental processes from products of complex & quaternionic induced Ginibre
ensembles

, Random Matrices Theor. Appl. 3, 1450014 (2014), arXiv:1404.4583 - Weak Commutation Relations & Eigenvalue Statistics for Products of Random
Matrices

, Phys. Rev. E 89, 032106 (2014), arXiv:1310.4154 - Products of Rectangular Random Matrices: Singular Values and Progressive
Scattering

, Phys. Rev. E 88, 052118 (2013), arXiv:1307.7560

Listed as ‘top publication’ by Google Scholar in 2017 and 2018 - Products of Independent Quaternion Ginibre Matrices and their Correlation
Functions

, J. Phys. A 46, 265201 (2013), arXiv:1301.3343 - Baryon Number Dirac Spectrum in QCD

, Phys. Rev. D 86, 014508 (2012), arXiv:1205.3093 - Recent exact and asymptotic results for products of independent random
matrices

, Acta Phys. Pol. B 46 1747 (2015), arXiv:1502.01667

Listed as ‘top publication’ by Google Scholar in 2016 , 2017 , 2018 and 2019 - The Laguerre Unitary Process

, Preprint, arXiv:1903.00176 - Consequences of Dale’s law on the stability-complexity relationship of random
neural networks

, Preprint, arXiv:1907.07293 - Products of Independent Gaussian Random Matrices

, Doctoral Dissertation, Bielefeld University, 2015, arXiv:1501.06128

Advisor: G. Akemann - QCD Sign Problem & Spectral Density of the Baryon Number Dirac Operator

, Master Thesis, University of Copenhagen, 2012

Advisor: K. Splittorff & P. H. Damgaard

- 2021---Now: Australian Research Council DECRA Fellow, University of Melbourne, Australia
- 2015---2020: ACEMS Research Fellow, University of Melbourne, Australia
- 2012---2015: PhD, Bielefeld-Beijing International Graduate College (IGK), Bielefeld University, Germany
- 2010---2012: MSc, Niels Bohr Institute, University of Copenhagen, Denmark
- 2007---2010: BSc, Niels Bohr Institute, University of Copenhagen, Denmark

- jesper[dot]ipsen[at]unimelb[dot]edu[dot]au
- School of Mathematics & Statistics, the University of Melbourne, Parkville, VIC 3010 AUSTRALIA