Wednesday, April 16, 2025 - 09:00 in Zoom
Universality for Random Matrices with an Edge Spectrum Singularity
A talk in the Seminar Zufallsmatrizen series by
Toby Shepherd
| Abstract: |
In their 2001 paper, Forrester-Witte showed, using Okamoto's tau-function theory, that the generating functional of the GUE with an edge spectrum singularity of order $|z-√2|^α$ is related to the $σ$-form of the Painlevé-II equation with coefficient $α$, generalising the result that was known for the edge of spectrum distribution for the GUE. We use a method of orthogonal polynomials to generalise this result to a class unitary ensembles with more general weight functions $exp(-n tr(V(M))$. In this talk I will introduce some background material on these ensembles and demonstrate firstly how we can obtain all of the asymptotic information for such ensembles by simply considering the large-n asymptotics of the relevant orthogonal polynomials.
Within the CRC this talk is associated to the project(s): C6 |
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