Wednesday, September 7, 2022 - 09:00 in ZOOM - Video Conference
The complex elliptic Ginibre ensemble at weak non-Hermiticity
A talk in the Seminar Zufallsmatrizen series by
Thomas Bothner from University of Bristol
| Abstract: |
In this talk we will focus on the complex elliptic Ginibre ensemble (eGinUE)
and analyze the statistical behavior of its eigenvalues in a suitable scaling
limit, known as the weak non-Hermiticity limit. In this limit the asymmetry
parameter in the model scales with the matrix dimension and the so
obtained 2D limiting point processes generalize the well-known sine and
Airy processes from the Gaussian unitary ensemble. Using integro-
differential Painlevé transcendents we will show how the gap functions of
the 2D limiting point processes can be evaluated in closed form and how
Riemann-Hilbert techniques can subsequently yield precise asymptotic
information for the same functions. Based on arXiv:2208.04684 and further
ongoing joint work with Alex Little.
Please contact Leslie Molag (leslie.molag@gmail.com) for details regarding access.
Within the CRC this talk is associated to the project(s): C6 |
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