“Dissertation Award 2022 for Dr. Markus Ebke”
The Bielefeld University Society for Excellence announced that Dr. Ebke will be awarded the 2022 Dissertation Prize for his dissertation entitled “Universal Scaling Limits of the Symplectic Elliptic Ginibre Ensemble.”
In his dissertation, Dr. Ebke studied the distribution of eigenvalues of large matrices with random entries.
It is already known that the corresponding mathematical model also describes clouds of charged particles in a two-dimensional world. Such a cloud of particles/eigenvalues is held in shape by an external potential, which in certain cases (when the matrices are normal) can be read off from the distribution of matrix entries.
Dr. Ebke’s main question was whether the external potential also has an effect on the distribution of particles within the cloud. Here, the matrix model has the additional property that the particles are repelled from an axis through the cloud. This situation is mathematically motivated by the use of quaternions, an extension of the complex numbers, for the matrix entries. For this so-called symplectic elliptic Ginibre ensemble, Dr. Ebke has found that deformation of the cloud does not affect the distribution near the axis. Moreover, the formulas for the distribution have a nice mathematical form that can be generalized to other matrix models.