Geodesic
Local laws for sparse sample covariance matrices without the truncation condition
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 32, Tome 510 (2022), pp. 65-86 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider sparse sample covariance matrices $\frac1{np_n}\mathbf X\mathbf X^*$, where $\mathbf X$ is a sparse matrix of order $n\times m$ with the sparse probability $p_n$. We prove the local Marchenko–Pastur law in some complex domain assuming that $np_n>\log^{\beta}n$, $\beta>0$ and some $(4+\delta)$-moment condition is fulfilled, $\delta>0$. 
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F. Götze; A. N. Tikhomirov; D. A. Timushev. Local laws for sparse sample covariance matrices without the truncation condition. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 32, Tome 510 (2022), pp. 65-86. http://geodesic.mathdoc.fr/item/ZNSL_2022_510_a3/

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