论文标题
艾森斯坦（Eisenstein
Quantum ergodicity for Eisenstein series on hyperbolic surfaces of large genus
论文作者
论文摘要
我们对有限区域双曲线表面的量子平均绝对偏差给出了定量估计，例如几何参数，例如属，尖和注射率半径。这意味着在有限区域的双曲线表面上，benjamini-schramm汇聚到双曲线平面的有限区域的倍曲表面上的量子性牙齿类型的量子化结果。我们表明，这是Mirzakhani相对于Weil-Petersson体积均匀选择的随机表面模型的通用。根据特定的表面序列，认为这给出了大多数尖端形式或爱森斯坦序列的）的结果。
We give a quantitative estimate for the quantum mean absolute deviation on hyperbolic surfaces of finite area in terms of geometric parameters such as the genus, number of cusps and injectivity radius. It implies a delocalisation result of quantum ergodicity type for eigenfunctions of the Laplacian on hyperbolic surfaces of finite area that Benjamini-Schramm converge to the hyperbolic plane. We show that this is generic for Mirzakhani's model of random surfaces chosen uniformly with respect to the Weil-Petersson volume. Depending on the particular sequence of surfaces considered this gives a result of delocalisation of most cusp forms or of Eisenstein series.
