论文标题
Toral Laplace本征函数和算术随机波的缺陷
The defect of toral Laplace eigenfunctions and Arithmetic Random Waves
论文作者
论文摘要
我们研究了在随机高斯场景中（“算术随机波”）或确定性的特征函数平均w.r.t。空间变量。在两种情况下，我们都利用了本征函数的相关对称性，以表明期望（高斯或空间）消失。我们的主要结果涉及缺陷方差的高能量限制行为。
We study the defect (or "signed area") distribution of toral Laplace eigenfunctions restricted to shrinking balls of radius above the Planck scale, in either random Gaussian scenario ("Arithmetic Random Waves"), or deterministic eigenfunctions averaged w.r.t. the spatial variable. In either scenario we exploit the associated symmetry of the eigenfunctions to show that the expectation (Gaussian or spatial) vanishes. Our principal results concern the high energy limit behaviour of the defect variance.
