About limiting spectral distributions of block-rescaled empirical covariance matrices

01/19/2022

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by   Gilles Mordant, et al.

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We establish that the limiting spectral distribution of a block-rescaled empirical covariance matrix is an arcsine law when the ratio between the dimension and the underlying sample size converges to 1 and when the samples corresponding to each block are independent. We further propose a conjecture for the cases where the latter ratio converges to a constant in the unit interval.