Presented By: Integrable Systems and Random Matrix Theory Seminar - Department of Mathematics
ISRMT Seminar: On Fredholm Pfaffians and Riemann-Hilbert problems
Amari Jaconelli (University of Bristol)
Abstract: In this talk, I will illustrate how classes of Fredholm Pfaffians, which can describe the eigenvalue distributions for orthogonal and symplectic matrix ensembles, can be computed in terms of canonical, auxiliary Riemann-Hilbert problems.
This is done by first algebraically manipulating the kernel of the Fredholm Pfaffian and then relating the resulting Pfaffian to a Riemann-Hilbert problem, assuming its main kernel is either of additive Hankel composition or truncated Wiener-Hopf type. One can then find asymptotic results for the Fredholm Pfaffian as a natural consequence of the Rieman-Hilbert problem characterisation.
This talk is based on my paper with Thomas Bothner, currently available in preprint on the arXiv: https://arxiv.org/abs/2511.23362.
To request access to the Zoom room, please contact Nathan Hayford at nhayford [ at ] umich.edu.
This is done by first algebraically manipulating the kernel of the Fredholm Pfaffian and then relating the resulting Pfaffian to a Riemann-Hilbert problem, assuming its main kernel is either of additive Hankel composition or truncated Wiener-Hopf type. One can then find asymptotic results for the Fredholm Pfaffian as a natural consequence of the Rieman-Hilbert problem characterisation.
This talk is based on my paper with Thomas Bothner, currently available in preprint on the arXiv: https://arxiv.org/abs/2511.23362.
To request access to the Zoom room, please contact Nathan Hayford at nhayford [ at ] umich.edu.
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