论文标题
大属表面模量空间的GOE统计数据
GOE statistics on the moduli space of surfaces of large genus
论文作者
论文摘要
对于紧凑的双曲线表面，我们定义了平滑的线性统计量，模仿了一个短的能量窗口中拉普拉斯特征值的数量。我们研究了此统计数据的差异，当对Weil-Petersson度量的所有属$ g $表面的模量$ \ mathcal m_g $进行平均时。我们表明，在双重限制中，首先采取了较大的属极限，然后是高能量限制，我们恢复了GOE统计。证据使Mirzakhani的集成公式的必不可少。
For a compact hyperbolic surface, we define a smooth linear statistic, mimicking the number of Laplace eigenvalues in a short energy window. We study the variance of this statistic, when averaged over the moduli space $\mathcal M_g$ of all genus $g$ surfaces with respect to the Weil-Petersson measure. We show that in the double limit, first taking the large genus limit and then the high energy limit, we recover GOE statistics. The proof makes essential use of Mirzakhani's integration formula.
