论文标题
稀疏样品协方差矩阵的地方法律，没有截断条件
Local Laws for Sparse Sample Covariance Matrices without the truncation condition
论文作者
论文摘要
我们考虑稀疏样本协方差矩阵$ \ frac1 {np_n} \ mathbf x \ mathbf x^*$，其中$ \ mathbf x $是订单$ n \ times m $的稀疏矩阵，带有稀疏的概率$ p_n $。假设$ np_n> \ log^βn$，$β> 0 $和一些$（4+δ）$ - 时刻条件已满足，$δ> 0 $，我们证明了某个复杂领域的本地Marchenko--pastur定律。
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, $δ>0$.
