Percolation on Homology Generators in Codimension One
Percolation on Homology Generators in Codimension One
复制标题
余维一中同调生成器的渗透
DOI：
10.1007/978-3-030-43408-3_12
复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Mikami Tatsuya
中科院分区：
文献类型：
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作者：
Hiraoka Yasuaki;Mikami Tatsuya
本文介绍了一种由高分子材料激发的新的渗流模型。该数学模型定义在d维空间中的随机立方集上，重点讨论了作为高维拓扑对象的（d-1）维孔的生成和分解。在这里，随机三次集是由单位面的并集构成的，这些面在d-1维中以概率p随机且独立地出现，而洞是由同调生成元来表示的。在此模型下，本文给出了空穴渗流临界概率的上、下估计，暗示了相变的存在。证明了无限空穴簇的唯一性。结果表明，在超临界相，对偶晶格中两点属于同一空穴簇的概率一致大于0。
This paper introduces a new percolation model motivated from polymer materials. The mathematical model is defined over a random cubical set in thed-dimensional spaceand focuses on generations and percolations of (d− 1)-dimensional holes as higher dimensional topological objects. Here, the random cubical set is constructed by the union of unit faces in dimensiond− 1 which appear randomly and independently with probabilityp, and holes are formulated by the homology generators. Under this model, the upper and lower estimates of the critical probabilityof the hole percolation are shown in this paper, implying the existence of the phase transition. The uniqueness of infinite hole cluster is also proven. This result shows that, in the supercritical phase,, the probabilitythat two points in the dual latticebelong to the same hole cluster is uniformly greater than 0.