This analysis uncovers the convergence rate of the spectral radius to a Gumbel distribution, implying mathematical insights on eigenvalues.
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 [34] 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]
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Ma et al. (2026) studied this question.
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