Events

Date: 29 October 2025   Time: 14:00 - 15:00

Location: MB-503, School of Mathematical Sciences, QMUL

The distributions of the extreme eigenvalue moduli are investigated for the complex Ginibre ensemble and its generalisation, the complex induced Ginibre ensemble, in the limit of very large dimensions of random matrices. The left and right tail distributions of the minimum modulus, for the complex Ginibre ensemble, are the Rayleigh and Weibull distributions, respectively. The scaled minimum modulus is Gumbel-distributed for the complex induced Ginibre ensemble specified with a proportional rectangularity index. It follows a Half-Normal Rayleigh distribution for the complex Ginibre ensemble. In this limit, the minimum modulus and the spectral radius are independent random variables for each of these non-Hermitian ensembles. The joint distribution of the eigenvalue moduli for the complex Ginibre ensemble is also explored. It is equal to the joint distribution of independent random variables, each following a Gamma-Rayleigh distribution. The main methods used are Andreief's integration formula and the methodological approach established by B. Rider at the edge of non-Hermitian ensembles.