论文标题
随机球形谐波节点长度的中等偏差估计值
Moderate Deviation estimates for Nodal Lengths of Random Spherical Harmonics
论文作者
论文摘要
我们证明了整个球体和缩小的球形域的随机球形谐波的节点长度的中等偏差估计值。最近在Marinucci，Rossi和Wigman（2020）和Todino（2020）（2020年）中建立了后者的中央限制定理。我们的证明是基于Schulte和Thäle（2016）的中等偏差原理的组合，用于生活在固定的Wiener混乱中的随机变量序列，基于指数等价的概念，其结果众所周知。
We prove Moderate Deviation estimates for nodal lengths of random spherical harmonics both on the whole sphere and on shrinking spherical domains. Central Limit Theorems for the latter were recently established in Marinucci, Rossi and Wigman (2020) and Todino (2020) respectively. Our proofs are based on the combination of a Moderate Deviation Principle by Schulte and Thäle (2016) for sequences of random variables living in a fixed Wiener chaos with a well-known result based on the concept of exponential equivalence.
