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Local Laws for Sparse Sample Covariance Matrices without the truncation condition
F. Götze, A. Tikhomirov, D. Timushev · 2022-09-27 · via math.PR updates on arXiv.org

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 $np_n>\log^βn$, $β>0$ and some $(4+δ)$-moment condition is fulfilled, $δ>0$.

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