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Teoriya Veroyatnostei i ee Primeneniya, 2023, Volume 68, Issue 4, Pages 813–833
DOI: https://doi.org/10.4213/tvp5668 (Mi tvp5668) 		 
Sufficient conditions for the Marchenko–Pastur theorem

P. A. Yaskov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.4213/tvp5668
Abstract: 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.
Keywords: random matrices, sample covariance matrices, the Marchenko–Pastur law.
Funding agency Grant number
Russian Science Foundation 23-11-00375
Received: 26.06.2023
Accepted: 18.09.2023
English version:
Theory of Probability and its Applications, 2024, Volume 68, Issue 4, Pages 657–673
DOI: https://doi.org/10.1137/S0040585X97T991696
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: P. A. Yaskov, “Sufficient conditions for the Marchenko–Pastur theorem”, Teor. Veroyatnost. i Primenen., 68:4 (2023), 813–833; Theory Probab. Appl., 68:4 (2024), 657–673
Citation in format AMSBIB
\Bibitem{Yas23}
\by P.~A.~Yaskov
\paper Sufficient conditions for the Marchenko--Pastur theorem
\jour Teor. Veroyatnost. i Primenen.
\yr 2023
\vol 68
\issue 4
\pages 813--833
\mathnet{http://mi.mathnet.ru/tvp5668}
\crossref{https://doi.org/10.4213/tvp5668}
\transl
\jour Theory Probab. Appl.
\yr 2024
\vol 68
\issue 4
\pages 657--673
\crossref{https://doi.org/10.1137/S0040585X97T991696}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85185322648}
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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