Gaussian Limits for Random Measures in Geometric Probability
Gaussian Limits for Random Measures in Geometric Probability
复制标题
几何概率中随机测量的高斯极限
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
J. Yukich
中科院分区：
文献类型：
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作者：
yuliy baryshnikov;J. Yukich
我们在d维空间中建立了由二项过程和Poisson点过程诱导的测度的高斯极限。极限高斯场具有依赖于点过程密度的协方差泛函。一般的中心极限定理被应用于由随机图(最近邻、Voronoi和影响范围图)、随机序列填充模型(弹道沉积和空间出生生长模型)和胚粒模型的统计诱导的度量。
We establish Gaussian limits for measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional which depends on the density of the point process. The general central limit theorems are applied to measures induced by random graphs (nearest neighbor, Voronoi, and sphere of influence graph), random sequential packing models (ballistic deposition and spatial birth growth models), and statistics of germ-grain models.