论文标题
高斯拉普拉斯本征functions的淋巴结成分计数的浓度
Concentration for nodal component count of Gaussian Laplace eigenfunctions
论文作者
论文摘要
我们研究了以下高斯拉普拉斯特征功能的结节组件计数：单色随机波（MRW）上的$ \ mathbb {r}^2 $，在$ \ mathbb {t}^2 $上，在$ \ mathbb {rsh）上对$ \ mathbb {t}^2 $上的算术随机波（arw）上$ \ mathbb {s}^2 $和$ \ mathbb {t}^2 $在$ \ mathbb {s}^2 $上的NODAL组件计数的指数浓度分别由Nazarov-Sodin和Rozenshein建立。在以下三种情况下，我们证明了节点组件计数的指数浓度：MRW在$ \ mathbb {r}^2 $中种植欧几里得球; RSH和ARW在$ \ Mathbb {s}^2 $和$ \ Mathbb {t}^2 $中，其半径略大于波长刻度。
We study nodal component count of the following Gaussian Laplace eigenfunctions: monochromatic random waves (MRW) on $\mathbb{R}^2$, arithmetic random waves (ARW) on $\mathbb{T}^2$ and random spherical harmonics (RSH) on $\mathbb{S}^2$. Exponential concentration for nodal component count of RSH on $\mathbb{S}^2$ and ARW on $\mathbb{T}^2$ were established by Nazarov-Sodin and Rozenshein respectively. We prove exponential concentration for nodal component count in the following three cases: MRW on growing Euclidean balls in $\mathbb{R}^2$; RSH and ARW on geodesic balls, in $\mathbb{S}^2$ and $\mathbb{T}^2$ respectively, whose radius is slightly larger than the wavelength scale.
