The suitably rescaled max |Z_j|^2 of eigenvalues of the product of k_n complex Ginibre matrices converges weakly to Phi_alpha for finite positive alpha = lim n/k_n, to Gumbel for alpha infinite, and to normal for alpha zero, with exact convergence rates in each regime.
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Precise convergence rate of spectral radius of product of complex Ginibre
The suitably rescaled max |Z_j|^2 of eigenvalues of the product of k_n complex Ginibre matrices converges weakly to Phi_alpha for finite positive alpha = lim n/k_n, to Gumbel for alpha infinite, and to normal for alpha zero, with exact convergence rates in each regime.