Descending chains, the lilypond model, and mutual-nearest-neighbour matching
Descending chains, the lilypond model, and mutual-nearest-neighbour matching
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降序链、百合池模型和相互最近邻匹配
DOI：
10.1239/aap/1127483738
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发表时间：
2005
影响因子：
1.2
通讯作者：
G. Last
中科院分区：
文献类型：
--
作者：
D. Daley;G. Last
我们考虑了ℝd中的一个硬球模型，它由一个驻点过程N和lilypond生长协议产生：在时间0，N的每个点开始以单位速度在所有方向上生长，形成一个球系统，其中任何一个特定的球在它与另一个球碰撞的瞬间停止它的生长。给出了一些非常一般的条件，在这些条件下，模型是定义良好的，没有渗流现象。没有渗流是因为，在我们的假设下，N中不可能有降级链。这一事实的证明构成了本文的重要部分。文中还指出，在没有降链的情况下，互最近邻匹配可以用来构造Thorisson定义的双射映射。
We consider a hard-sphere model in ℝ d generated by a stationary point process N and the lilypond growth protocol: at time 0, every point of N starts growing with unit speed in all directions to form a system of balls in which any particular ball ceases its growth at the instant that it collides with another ball. Some quite general conditions are given, under which it is shown that the model is well defined and exhibits no percolation. The absence of percolation is attributable to the fact that, under our assumptions, there can be no descending chains in N. The proof of this fact forms a significant part of the paper. It is also shown that, in the absence of descending chains, mutual-nearest-neighbour matching can be used to construct a bijective point map as defined by Thorisson.