论文标题
部分可观测时空混沌系统的无模型预测
Rank-uniform local law for Wigner matrices
论文作者
论文摘要
我们证明了Wigner矩阵的一般地方法律，该法律可以最佳地处理任意等级的可观察物，因此统一了众所周知的平均和各向同性的地方法律。作为一个应用程序，我们证明了Wigner矩阵的批量特征向量的一般确定性矩阵$ a $的二次形式大约具有高斯波动。因此，对于批量频谱，我们概括了先前的结果[Arxiv：2103.06730]有效的测试矩阵$ a $ a $ a $ a $ a $ a $以及benigni和Lopatto [arxiv：2103.12013]的结果，对特定的小等级可观察物有效。
We prove a general local law for Wigner matrices which optimally handles observables of arbitrary rank and thus it unifies the well-known averaged and isotropic local laws. As an application, we prove that the quadratic forms of a general deterministic matrix $A$ on the bulk eigenvectors of a Wigner matrix has approximately Gaussian fluctuation. For the bulk spectrum, we thus generalize our previous result [arXiv:2103.06730] valid for test matrices $A$ of large rank as well as the result of Benigni and Lopatto [arXiv:2103.12013] valid for specific small rank observables.
