论文标题
浆果淋巴结长度的功能收敛：近似紧密度和总障碍
Functional Convergence of Berry's Nodal Lengths: Approximate Tightness and Total Disorder
论文作者
论文摘要
我们考虑Berry的随机平面波模型（1977），并证明了空间功能极限定理 - 在高能量极限中 - 用于通过将其淋巴结长度限制为矩形域获得的随机场的离散和截断版本。我们的分析至关重要，基于对淋巴结长度在所谓的第二维纳混乱上的投影的详细研究，其高能波动由多边形曲线索引的高斯总疾病场给出。然后将这种确切的表征与固定高斯随机场上的上流区域的矩估计相结合，并具有Davydov和Zikikitis（2005）的紧密标准。
We consider Berry's random planar wave model (1977), and prove spatial functional limit theorems - in the high-energy limit - for discretized and truncated versions of the random field obtained by restricting its nodal length to rectangular domains. Our analysis is crucially based on a detailed study of the projection of nodal lengths onto the so-called second Wiener chaos, whose high-energy fluctuations are given by a Gaussian total disorder field indexed by polygonal curves. Such an exact characterization is then combined with moment estimates for suprema of stationary Gaussian random fields, and with a tightness criterion by Davydov and Zikitis (2005).
