论文标题
Wigner矩阵的CLT中几乎最佳的规律条件
Almost-optimal bulk regularity conditions in the CLT for Wigner matrices
论文作者
论文摘要
我们考虑$ \ mathrm {tr}（φ（h））$的线性光谱统计量，用于测试功能的低规律性和Wigner矩阵的$φ$，并具有平稳的入口分布。我们表明，对于功能，在sobolev空间中$ h^{1/2+\ varepsilon} $或空间$ c^{1/2+\ varepsilon} $，这些光谱分布中的光谱分布中得到了这些线性光谱统计的较高的常规变量，这些频谱均具有较高的速度，并具有较高的差异。 $ \ varepsilon> 0 $。
We consider linear spectral statistics of the form $\mathrm{tr} ( φ(H))$ for test functions $φ$ of low regularity and Wigner matrices $H$ with smooth entry distribution. We show that for functions $φ$ in the Sobolev space $H^{1/2+\varepsilon}$ or the space $C^{1/2+\varepsilon}$, that are supported within the spectral bulk of the semicircle distribution, these linear spectral statistics have asymptotic Gaussian fluctuations with the same variance as in the CLT for functions of higher regularity, for any $\varepsilon >0$.
