The scaled spectral radius of products of k_n complex Ginibre n-by-n matrices converges weakly to a continuous family Phi_alpha of limiting distributions that interpolates between the standard normal (alpha=0) and Gumbel (alpha=infty) laws, with exact convergence rates.
From the Littlewood-Offord problem to the circular law: universality of the spectral distribution of random matrices.Bull
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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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From Gaussian to Gumbel: extreme eigenvalues of complex Ginibre products with exact rates
The scaled spectral radius of products of k_n complex Ginibre n-by-n matrices converges weakly to a continuous family Phi_alpha of limiting distributions that interpolates between the standard normal (alpha=0) and Gumbel (alpha=infty) laws, with exact convergence rates.