Nodal densities of planar gaussian random waves
Nodal densities of planar gaussian random waves
复制标题
平面高斯随机波的节点密度
DOI：
10.1140/epjst/e2007-00156-1
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Mark R. Dennis
中科院分区：
文献类型：
--
作者：
Mark R. Dennis
抽象的。
回顾了高斯随机函数的节点密度，对各种物理系统（包括混沌量子本征函数和光学散斑图案）进行建模。
各向同性随机实函数和复函数的节点域根据其 Minkowski 泛函进行公式化，并讨论了它们的相关性和谱。
回顾了二维实函数和复函数及其导数的零点统计密度的结果。
在二维随机表面的 hessian 行列式（高斯曲率）的节点域上得出了新结果。
Abstract.
The nodal densities of gaussian random functions, modelling various physical systems including chaotic quantum eigenfunctions and optical speckle patterns, are reviewed.
The nodal domains of isotropically random real and complex functions are formulated in terms of their Minkowski functionals, and their correlations and spectra are discussed.
The results on the statistical densities of the zeros of the real and complex functions, and their derivatives, in two dimensions are reviewed.
New results are derived on the nodal domains of the hessian determinant (gaussian curvature) of two-dimensional random surfaces.