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Necessary and sufficient conditions for the Marchenko-Pastur theorem. (English) Zbl 1352.60008

Summary: We obtain necessary and sufficient conditions for the Marchenko-Pastur theorem for matrices with IID isotropic rows. Our conditions are related to a weak concentration property for certain quadratic forms of the rows.

MSC:

60B20 Random matrices (probabilistic aspects)
15B52 Random matrices (algebraic aspects)
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Full Text: DOI Euclid