论文标题
部分可观测时空混沌系统的无模型预测
The least singular value of the general deformed Ginibre ensemble
论文作者
论文摘要
我们研究了$ n \ times n $矩阵$ h-z $的最低奇异价值，其中$ h = a_0+h_0 $，其中$ h_0 $是从带有iid高斯条目的复杂的矩阵集合中汲取的，$ a_0 $ a_0 $是一般的$ n \ times $ n \ times $ n \ times n $ n $ itrix and complects $ tase us $ a $ sys $ sy是独立于$）。假设在$ A_0 $上有一些相当普遍的假设，我们证明了最佳的尾巴估计值在$ h $的频谱边缘围绕$ h $的光谱边缘，因此将Cipolloni，Erdős，SchröderArxiv：1908.01653推广到Case $ A_0 $ a_0 \ ne 0 $ 0 $ 0 $ 0 $。结果改善了Sankar，Spielman和Teng的经典约束。
We study the least singular value of the $n\times n$ matrix $H-z$ with $H=A_0+H_0$, where $H_0$ is drawn from the complex Ginibre ensemble of matrices with iid Gaussian entries, and $A_0$ is some general $n\times n$ matrix with complex entries (it can be random and in this case it is independent of $H_0$). Assuming some rather general assumptions on $A_0$, we prove an optimal tail estimate on the least singular value in the regime where $z$ is around the spectral edge of $H$ thus generalize the recent result of Cipolloni, Erdős, Schröder arxiv:1908.01653 to the case $A_0\ne 0$. The result improves the classical bound by Sankar, Spielman and Teng.
