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Seminar
FIELD Mathematics
DATE June 18 (Fri), 2021
TIME 17:00-18:00
PLACE Online
SPEAKER Markus Ebke
HOST Lee, Jaehun
INSTITUTE  
TITLE [GS_M_APP] Symplectic non-Hermitian random matrices - Skew-orthogonal polynomials and universal scaling limits
ABSTRACT

Non-Hermitian random matrices with symplectic symmetry provide examples for Pfaffian point processes in the complex plane. They are characterised by a matrix-valued kernel of skew-orthogonal polynomials, however finding an appropriate set of polynomials for a given matrix ensemble is difficult.
In this talk I will present an explicit construction of skew-orthogonal polynomials in terms of orthogonal polynomials that satisfy a three-term recurrence relation. Additionally, for the symplectic elliptic Ginibre ensemble I will show how to compute the microscopic large-N limit of the kernel at the origin and prove its universality.
This is based on joint work with Gernot Akemann and Iv?n Parra. If time permits, I will also mention some results from an ongoing project with Sung-Soo Byun.

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