论文标题
算术随机波的淋巴结长度的非世界性中度偏差原理
Non-Universal Moderate Deviation Principle for the Nodal Length of Arithmetic Random Waves
论文作者
论文摘要
受到最近工作的启发[MRT21]，我们证明了整个歧管和收缩的摩托区域上的算术随机波的淋巴结长度（标准扁平圆环上的高斯拉普拉斯特征函数），这证明了算术随机波的淋巴结长度（高斯拉普拉斯特征函数）。通过混乱的扩张，数量理论估计值和完全相关现象，分别在[MPRW16]和[BMW20]中分别建立了后者的二阶波动。我们的证明很简单，依赖于算术随机波的长期记忆行为与淋巴结长度的混乱膨胀以及大偏差理论中众所周知的技术（收缩原理和指数等效性的概念）之间的相互作用。
Inspired by the recent work [MRT21], we prove a non-universal non-central Moderate Deviation principle for the nodal length of arithmetic random waves (Gaussian Laplace eigenfunctions on the standard flat torus) both on the whole manifold and on shrinking toral domains. Second order fluctuations for the latter were established in [MPRW16] and [BMW20] respectively, by means of chaotic expansions, number theoretical estimates and full correlation phenomena. Our proof is simple and relies on the interplay between the long memory behavior of arithmetic random waves and the chaotic expansion of the nodal length, as well as on well-known techniques in Large Deviation theory (the contraction principle and the concept of exponential equivalence).
