论文标题
大型矩阵随机扰动的特征值差距
Eigenvalue Gaps of Random Perturbations of Large Matrices
论文作者
论文摘要
当前的工作适用于Jain的一些最新组合工具，以控制矩阵$ m_n = m + n_n $的特征值差距，其中$ m $是确定性的，与大型运算符规范对称，$ n_n $是一个随机的对称矩阵，带有Subgaussian零件。我们的尾部边界的结果之一是，$ m_n $具有简单的频谱，概率至少$ 1- \ exp（-n^{2/15}）$，它以nguyen，tao和vu的结果来改善，而nguyen，tao和vu的概率和矩阵$ m $的尺寸也可以提高。
The current work applies some recent combinatorial tools due to Jain to control the eigenvalue gaps of a matrix $M_n = M + N_n$ where $M$ is deterministic, symmetric with large operator norm and $N_n$ is a random symmetric matrix with subgaussian entries. One consequence of our tail bounds is that $M_n$ has simple spectrum with probability at least $1 - \exp(-n^{2/15})$ which improves on a result of Nguyen, Tao and Vu in terms of both the probability and the size of the matrix $M$.
