Geodesic
Local Marchenko--Pastur law for sparse rectangular random matrices
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 501 (2021), pp. 22-25

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We consider sparse sample covariance matrices with sparsity probability $p_n\ge c_0\log^{\frac2\kappa}n/n$ with $\kappa>0$. Assuming that the distribution of matrix elements has a finite absolute moment of order $4+\delta$, $\delta>0$, it is shown that the distance between the Stieltjes transforms of the empirical spectral distribution function and the Marchenko–Pastur law is of order $\log n(1/(nv)+1/(np_n))$, где where $v$ is the distance to the real axis in the complex plane.
Keywords: local Marchenko–Pastur law, local regime, sparse random matrices, spectrum of a random matrix, Stieltjes transform. 
@article{DANMA_2021_501_a3,
     author = {F. G\"otze and D. A. Timushev and A. N. Tikhomirov},
     title = {Local {Marchenko--Pastur} law for sparse rectangular random matrices},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {22--25},
     publisher = {mathdoc},
     volume = {501},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_501_a3/}
}
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F. Götze; D. A. Timushev; A. N. Tikhomirov. Local Marchenko--Pastur law for sparse rectangular random matrices. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 501 (2021), pp. 22-25. http://geodesic.mathdoc.fr/item/DANMA_2021_501_a3/