Wednesday, July 12, 2023 - 09:00 in ZOOM - Video Conference
Disk counting statistics of the eigenvalues of truncated unitary matrices
A talk in the Seminar Zufallsmatrizen series by
Philippe Moreillon
| Abstract: |
In this talk, I will present new results on the disk counting statistics of the
eigenvalues of truncated unitary matrices. More specifically, if T is the
upper-left submatrix of a Haar distributed unitary matrix of size $(n+k) x
(n+k)$, we prove that as n tends to infinity with k fixed, the associated
moment generating function verifies asymptotics of the form $exp(C_1 n +
C_2 + o(1))$, where the constants $C_1$ and $C_2$ are given in terms of the
incomplete Gamma function. Our proof relies on the uniform asymptotics of
the incomplete Beta function.
This talk is based on a joint work with Christophe Charlier and
Yacin Ameur.
Please contact Lucas Hackl
(Lucas.Hackl@unimelb.edu.au) for details regarding access
Within the CRC this talk is associated to the project(s): C6 |
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