# Markus Ebke: Skew-Orthogonal Polynomials for Quaternion Non-Hermitian Random Matrices

**Time: **
Thu 2019-10-03 16.15 - 17.00

**Lecturer: **
Markus Ebke (Bielefeld University)

**Location: ** F11, KTH

### Abstract

In 1965 J. Ginibre introduced three non-hermitian random matrix ensembles with i.i.d. Gaussian distributed elements (real, complex and quaternion). The distribution can be generalized and today there are many results known for the complex case. In my talk I want to discuss the quaternion case. I will introduce quaternion non-hermitian random matrices and explain how skew-orthogonal polynomials (introduced by E.Kanzieper in 2002) can be used to express the eigenvalue correlation functions. I will show some new results for general weight functions (where the orthogonal polynomials fulfill a three-step recurrence relation) and for the elliptic Ginibre ensemble (based on a Mehler-formula for skew-orthogonal polynomials). If time permits, I will also mention the chiral elliptic Ginibre ensemble that was examined by G. Akemann in 2005.