Wednesday, January 8, 2025 - 09:00 in Zoom
Asymptotic Expansions in Random Matrix Theory: A Perplexing Layer of Integrability at the Soft Edge
A talk in the Seminar Zufallsmatrizen series by
Folkmar Bornemann
| Abstract: |
In studying higher-order finite-size corrections to various limit laws at the soft edge, we discovered a particularly simple yet perplexing structure: the correction terms are linear combinations of higher-order derivatives of the limit law with rational polynomial coefficients. Given the highly nonlinear nature of perturbations of operator determinants, such a result is unexpected and points to a further layer of integrability. Here, it is the unique solvability of certain rectangular linear systems over the ring of rational polynomials with the solution of Painlevé II and its derivative added as indeterminates. We will present the ideas and evidence in the simplest example, the large matrix limit of Gaussian ensembles.
Within the CRC this talk is associated to the project(s): C6 |
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