论文标题
紧凑表面和光滑线性光谱统计的随机覆盖物
Random covers of compact surfaces and smooth linear spectral statistics
论文作者
论文摘要
我们考虑随机的n-covers $ x_n $的任意紧凑双曲表面$ x $。我们表明，在较大的N型和小窗口限制中，laplacian的平滑光谱统计差异被统一的阿贝尔角色扭曲，遵守GOE和GUE随机矩阵的普遍定律，取决于角色保留或打破时间反向对称性。我们还证明了在紧凑型线性基团中价值的更高维曲折的概括。这些结果证实了浆果的猜想，并且是鲁德尼克最近作品的Weil-Petersson随机表面模型的离散类似物。
We consider random n-covers $X_n$ of an arbitrary compact hyperbolic surface $X$. We show that in the large n regime and small window limit, the variance of the smooth spectral statistics of the Laplacian twisted by a unitary abelian character, obey the universal laws of GOE and GUE random matrices, depending on wether the character preserves or breaks the time reversal symmetry. We also prove a generalization for higher dimensional twists valued in compact linear groups. These results confirm a conjecture of Berry and is a discrete analog of a recent work of Rudnick for the Weil-Petersson model of random surfaces.
