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Matches in SemOpenAlex for { <https://semopenalex.org/work/W1995241424> ?p ?o ?g. }

• W1995241424 abstract "We consider sample covariance matrices of the form $X^*X$, where $X$ is an $M times N$ matrix with independent random entries. We prove the isotropic local Marchenko-Pastur law, i.e. we prove that the resolvent $(X^* X - z)^{-1}$ converges to a multiple of the identity in the sense of quadratic forms. More precisely, we establish sharp high-probability bounds on the quantity $langle v , (X^* X - z)^{-1}wrangle - langle v , wrangle m(z)$, where $m$ is the Stieltjes transform of the Marchenko-Pastur law and $v , w in mathbb{C}^N$. We require the logarithms of the dimensions $M$ and $N$ to be comparable. Our result holds down to scales $Im z geq N^{-1+varepsilon}$ and throughout the entire spectrum away from 0. We also prove analogous results for generalized Wigner matrices." @default.
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• W1995241424 date "2014-01-01" @default.
• W1995241424 modified "2023-10-18" @default.
• W1995241424 title "Isotropic local laws for sample covariance and generalized Wigner matrices" @default.
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• W1995241424 doi "https://doi.org/10.1214/ejp.v19-3054" @default.
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