Crack STIT tessellations: characterization of stationary random tessellations stable with respect to iteration
Crack STIT tessellations: characterization of stationary random tessellations stable with respect to iteration
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Crack STIT tessellations：表征相对于迭代稳定的平稳随机曲面细分
DOI：
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发表时间：
2005
影响因子：
1.2
通讯作者：
V. Weiß
中科院分区：
文献类型：
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作者：
W. Nagel;V. Weiß
我们的主要结果是证明了d维欧氏空间中随机平稳格子集的存在，并且具有如下稳定性：它们的分布不随格子格的迭代(或嵌套)的操作而改变。该操作意味着给定细分的单元被独立的、相同分布的细分单独细分，从而产生新的细分。还证明了对于任意平稳镶嵌，由重复重标度迭代生成的序列弱收敛于这样的稳定镶嵌，从而完全刻画了这类稳定的平稳镶嵌。
Our main result is the proof of the existence of random stationary tessellations in d-dimensional Euclidean space with the following stability property: their distribution is invariant with respect to the operation of iteration (or nesting) of tessellations with an appropriate rescaling. This operation means that the cells of a given tessellation are individually and independently subdivided by independent, identically distributed tessellations, resulting in a new tessellation. It is also shown that, for any stationary tessellation, the sequence that is generated by repeated rescaled iteration converges weakly to such a stable tessellation; thus, the class of all stable stationary tessellations is fully characterized.