标题： 大型随机矩阵的大秩扰动的特征值渐近行为 显示英文标题

标题： Asymptotic behavior of eigenvalues of large rank perturbations of large random matrices

摘要： 本文涉及变形的Wigner随机矩阵。 这些矩阵与深度神经网络（DNNs）密切相关：训练后的DNN的权重矩阵可以表示为$R + S$的形式，其中$R$是随机的，而$S$是高度相关的。 此类矩阵的谱在基于随机矩阵理论的新剪枝技术的严格支撑中起着关键作用。 数学研究仅针对有限秩矩阵$S$。 然而，在实际中秩可能会增长。 在本文中，我们为秩增长的情况开发了渐近分析。 显示英文摘要

摘要： The paper is concerned with deformed Wigner random matrices. These matrices are closely connected with Deep Neural Networks (DNNs): weight matrices of trained DNNs could be represented in the form $R + S$, where $R$ is random and $S$ is highly correlated. The spectrum of such matrices plays a key role in rigorous underpinning of the novel pruning technique based on Random Matrix Theory. Mathematics has been done only for finite-rank matrix $S$. However, in practice rank may grow. In this paper we develop asymptotic analysis for the case of growing rank.