Exact convergence rate of spectral radius of complex Ginibre to Gumbel distribution
Abstract
Consider the complex Ginibre ensemble, whose eigenvalues are [Formula: see text] and the spectral radius [Formula: see text] Set [Formula: see text] and [Formula: see text] be its distribution function, where [Formula: see text] It was proved in Rider [A limit theorem at the edge of a non-Hermitian random matrix ensemble, J. Phys. A 36 (2003) 3401–3409] that [Formula: see text] converges weakly to the Gumbel distribution [Formula: see text] whose distribution function [Formula: see text] We prove in further in this paper that [Formula: see text] and the Berry–Esseen bound [Formula: see text]
Fields of Study & Subjects
Random Matrices and Applications
Mathematical functions and polynomials
Graph theory and applications
Publication details
- Journal / source
- Random Matrices Theory and Application
- Publisher
- World Scientific Pub Co Pte Ltd
- Volume
- 15
- Issue
- 02
- Publication date
- 24 January 2026
- Language
- EN