In this text, based on elementary computations, we provide a perturbative expansion of the coordinates of the eigenvectors of a Hermitian matrix of large size perturbed by a random matrix with small operator norm whose entries in the eigenvector basis of the first one are independent, centered, with a variance profile. This is done through a perturbative expansion of spectral measures associated to the state defined by a given vector.

中文翻译：

---

随机扰动下矩阵的特征向量

在本文中，基于基本计算，我们提供了一个大尺寸厄米特矩阵的特征向量坐标的微扰展开，该矩阵被一个具有小算子范数的随机矩阵扰动，其第一个特征向量基中的条目是独立的、居中的，具有方差轮廓。这是通过与给定向量定义的状态相关的频谱测量的微扰扩展来完成的。