Geodesic
Sufficient conditions for the Marchenko--Pastur theorem
Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 4, pp. 813-833

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We find general sufficient conditions in the Marchenko–Pastur theorem for high-dimensional sample covariance matrices associated with random vectors, for which the weak concentration property of quadratic forms may not hold in general. The results are obtained by means of a new martingale method, which may be useful in other problems of random matrix theory.
Mots-clés : random matrices
Keywords: sample covariance matrices, the Marchenko–Pastur law. 
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     author = {P. A. Yaskov},
     title = {Sufficient conditions for the {Marchenko--Pastur} theorem},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     publisher = {mathdoc},
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     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2023_68_4_a8/}
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P. A. Yaskov. Sufficient conditions for the Marchenko--Pastur theorem. Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 4, pp. 813-833. http://geodesic.mathdoc.fr/item/TVP_2023_68_4_a8/