费米子本征矢矩流
Fermionic eigenvector moment flow
摘要：
我们展示了新的功能的戴森布朗运动的特征向量遵循一个方程类似的Bourgade-Yau特征向量矩流。这些观测量可以被看作是原始（玻色子）观测量的费米对应物。通过分析费米和玻色子观测量，我们得到了新的本征向量之间的相关性。波动$\sum_{α\in I}u_k(α)^2-{\vert I\vert}/{N}$解相关的不同的特征向量的尺寸$N$的增长和最佳估计的部分内积$\sum_{α\in I}u_k(α)u_\ell(α)$之间的两个特征向量。这些静态结果得到的可积动力学广义维格纳矩阵，并应适用于广泛的类平均场模型。
英文摘要：
We exhibit new functions of the eigenvectors of the Dyson Brownian motion which follow an equation similar to the Bourgade-Yau eigenvector moment flow. These observables can be seen as a Fermionic counterpart to the original (Bosonic) ones. By analyzing both Fermionic and Bosonic observables, we obtain new correlations between eigenvectors. The fluctuations $\sum_{α\in I}u_k(α)^2-{\vert I\vert}/{N}$ decorrelate for distinct eigenvectors as the dimension $N$ grows and an optimal estimate on the partial inner product $\sum_{α\in I}u_k(α)u_\ell(α)$ between two eigenvectors is given. These static results obtained by integrable dynamics are stated for generalized Wigner matrices and should apply to wide classes of mean field models.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
