Markus Ebke

I am a doctoral student in Prof. Gernot Akemann's group. My research topic is the integrability of non-hermitian random matrix ensembles.

What is that?
Imagine you start with an ensemble of NxN random matrices. You want to analyse the distribution of the eigenvalues (e.g. the density). Write it down as an N-fold integral over the joint probability density of the eigenvalues. Now if you solve all of these integrals, your analysis will be much easier. But solving integrals is hard! And you have N of them! You need to find a clever way to compute the integrals.
And here my research can help you. If your matrix model is one of the models that I am researching, otherwise: Good luck!

Contact

Office: E5-133
E-mail: markus.ebke(at)uni-bielefeld.de
PO Box: #217 (Room V3-128)

Research Interests

Random matrix theory with focus on applications in physics.
Currently I am working with quaternionic non-hermitian random matrices that are an extension of Ginibre's quaternion ensemble. I research ways to find the skew-orthogonal polynomials that are used to solve these ensembles and how to compute their large-N limit.

Research Stays

  • September 29 - October 5, 2019: KTH in Stockholm, Sweden. I gave a talk in their Random Matrix Theory Seminar on October 3.
  • June 21 - September 5, 2021: KAIST in Daejeon, South Korea. I joined the research group of Prof. Ji Oon Lee.
  • August 14 - 22, 2021: KIAS in Seoul, South Korea. I was invited by Dr. Song-Mi Seo and Sung-Soo Byun.

Conferences and Talks

Publications

  • (with Gernot Akemann and Iván Parra) Skew-orthogonal polynomials in the complex plane and their Bergman-like kernels, arXiv:2103.12114 (preprint)
  • (with Sung-Soo Byun) Universal scaling limits of the symplectic elliptic Ginibre ensemble, arxiv:2108.05541 (preprint)

Page Tools