Percolation and limit theory for the poisson lilypond model
Percolation and limit theory for the poisson lilypond model
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泊松百合池模型的渗流和极限理论
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
M. Penrose
中科院分区：
文献类型：
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作者：
G. Last;M. Penrose
d空间中点过程的lilypond模型是一个以点为中心的非重叠球的增长极大系统。建立了关于扩展窗口上的泊松过程或二项式点过程序列的Lilypond模型的总体积和组分数的中心极限定理。对于齐次Poisson过程上的Lilypond模型，我们给出了原点处簇大小的次指数衰减尾界。最后，我们考虑了增强的Poisson lilypond模型，其中所有的球都被放大了一个固定的量（增强参数），并证明了对于d > 1，这个参数的临界值，在此之上，增强模型是严格正的。© 2012 Wiley Periodicals，Inc.随机结构算法，2012
The lilypond model on a point process in d ‐space is a growth‐maximal system of non‐overlapping balls centred at the points. We establish central limit theorems for the total volume and the number of components of the lilypond model on a sequence of Poisson or binomial point processes on expanding windows. For the lilypond model over a homogeneous Poisson process, we give subexponentially decaying tail bounds for the size of the cluster at the origin. Finally, we consider the enhanced Poisson lilypond model where all the balls are enlarged by a fixed amount (the enhancement parameter), and show that for d > 1 the critical value of this parameter, above which the enhanced model percolates, is strictly positive. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012