Jesper Photo

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.

Publication List Google Scholar


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.


    Research articles
  1. A generalisation of the relation between zeros of the complex Kac polynomial and eigenvalues of truncated unitary matrices
    P. J. Forrester & J. R. Ipsen, Probab. Theor. Rel. Fields 175 (2019) 833 , arXiv:1807.06743
  2. Multiplicative convolution of real asymmetric and real antisymmetric matrices
    M. Kieburg, P. J. Forrester, J. R. Ipsen, Adv. Pure Appl. Math. 10 (2019) 467, arXiv:1712.04916
  3. Orthogonal and symplectic Harish-Chandra integrals and matrix product ensembles
    P. J. Forrester, J. R. Ipsen, D.-Z. Liu, & L. Zhang, Random Matrices Theor. Appl. 08 (2019) 1950015, arXiv:1711.10691
  4. Kac-Rice fixed point analysis for single-and multi-layered complex systems
    J. R. Ipsen & P. J. Forrester,, Random J. Phys. A 51 (2018) 474003, arXiv:1807.05790
    Invited contribution to Special Issue: Random Matrices, the first 90 years
  5. How many eigenvalues of a product of truncated orthogonal matrices are real?
    P. J. Forrester, J. R. Ipsen, & S. Kumar, Experiment. Math. (2018) 1, arXiv:1708.00967
  6. Matrix Product ensembles of Hermite-type and the hyperbolic Harish-Chandra–Itzykson–Zuber integral
    P. J. Forrester, J. R. Ipsen, & D.-Z. Liu, Ann. Henri Poincaré 19 (2018) 1307, arXiv:1702.07100
  7. Selberg integral theory and Muttalib-Borodin ensembles
    P. J. Forrester & J. R. Ipsen, Adv. Appl. Math. 95 (2018) 152, arXiv:1612.06517
  8. May–Wigner transition in large random dynamical systems
    J. R. Ipsen, J. Stat. Mech. (2017) 093209, arXiv:1705.05047
  9. Real eigenvalue statistics for products of asymmetric real Gaussian matrices
    P. J. Forrester & J. R. Ipsen, Lin. Alg. Appl. 510 259 (2016), arXiv:1608.04097
  10. Isotropic Brownian motion over complex fields as a solvable model for May–Wigner stability analysis
    J. R. Ipsen & H. Schomerus, J. Phys. A 49 385201 (2016), arXiv:1602.06364
  11. Lyapunov exponents for products of rectangular real,complex & quaternionic Ginibre matrices
    J. R. Ipsen, J. J. Phys. A 48, 155204 (2015), arXiv:1412.3003 Publisher's pick
  12. Permanental processes from products of complex & quaternionic induced Ginibre ensembles
    G. Akemann, J. R. Ipsen & E. Strahov, Random Matrices Theor. Appl. 3, 1450014 (2014), arXiv:1404.4583
  13. Weak Commutation Relations & Eigenvalue Statistics for Products of Random Matrices
    J. R. Ipsen & M. Kieburg, Phys. Rev. E 89, 032106 (2014), arXiv:1310.4154
  14. Products of Rectangular Random Matrices: Singular Values and Progressive Scattering
    G. Akemann, J. R. Ipsen & M. Kieburg, Phys. Rev. E 88, 052118 (2013), arXiv:1307.7560
    Listed as ‘top publication’ by Google Scholar in 2017 and 2018
  15. Products of Independent Quaternion Ginibre Matrices and their Correlation Functions
    J. R. Ipsen, J. Phys. A 46, 265201 (2013), arXiv:1301.3343
  16. Baryon Number Dirac Spectrum in QCD
    J. R. Ipsen & K. Splittorff, Phys. Rev. D 86, 014508 (2012), arXiv:1205.3093
  17. Review articles
  18. Recent exact and asymptotic results for products of independent random matrices
    G. Akemann & J. R. Ipsen, Acta Phys. Pol. B 46 1747 (2015), arXiv:1502.01667
    Listed as ‘top publication’ by Google Scholar in 2016 , 2017 , 2018 and 2019
  19. arXiv preprints
  20. The Laguerre Unitary Process
    J. R. Ipsen, Preprint, arXiv:1903.00176
  21. Consequences of Dale’s law on the stability-complexity relationship of random neural networks
    J. R. Ipsen & A. D. H. Peterson, Preprint, arXiv:1907.07293
  22. Theses
  23. Products of Independent Gaussian Random Matrices
    J. R. Ipsen, Doctoral Dissertation, Bielefeld University, 2015, arXiv:1501.06128
    Advisor: G. Akemann
  24. QCD Sign Problem & Spectral Density of the Baryon Number Dirac Operator
    J. R. Ipsen, Master Thesis, University of Copenhagen, 2012
    Advisor: K. Splittorff & P. H. Damgaard