细胞分裂过程的一致性
On the consistency of cell division processes
摘要：
针对一类细胞分裂过程，研究了欧几里得空间$\mathbb{R}^d$的空间一致性.这解决了限制于有界集$V$的这些镶嵌的分布是否取决于执行单元分裂过程的构造的较大区域$W\supset V$的选择的问题。这也可以理解为细胞分裂过程中的边界效应问题。在Nagel和Weiwei（2005）中，STIT镶嵌是空间上一致的。有迹象表明STIT镶嵌过程可能是唯一具有这种一致性属性的不变性细胞分裂过程。在本文中，它表明，在一个合理的广泛的类细胞分裂过程中，STIT镶嵌是唯一的是一致的。
英文摘要：
For a class of cell division processes, generating tessellations of the Euclidean space $\mathbb{R}^d$, spatial consistency is investigated. This addresses the problem whether the distribution of these tessellations, restricted to a bounded set $V$, depends on the choice of a larger region $W\supset V$ where the construction of the cell division process is performed. This can also be understood as the problem of boundary effects in the cell division procedure. In Nagel and Weiß (2005) it was shown that the STIT tessellations are spatially consistent There were hints that the STIT tessellation process might be the only translation-invariant cell division process that has such a consistency property. In the present paper it is shown that, within a reasonable wide class of cell division processes, the STIT tessellations are the only ones that are consistent.
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