论文标题
脸和周期渗透
Face and cycle percolation
论文作者
论文摘要
我们认为面部和循环渗透是基于欧几里得空间中随机简单复合物的连续渗透模型。面部渗透是通过共享$（D-1）$ - 尺寸的面孔的无限序列来定义的。相比之下，循环渗透需要无限$ d $ cycles的存在，从而概括了plaquette渗透的晶格概念。我们讨论面部渗透的尖锐相变，并得出面部和周期渗透的临界强度之间的比较结果。最后，我们考虑了单纯渗透的替代版本，每当他们彼此之间足够接近时，就会声明简单为邻居，并证明涉及此替代版本的关键强度和面部渗透的严格强度的严格不平等。
We consider face and cycle percolation as models for continuum percolation based on random simplicial complexes in Euclidean space. Face percolation is defined through infinite sequences of $d$-simplices sharing a $(d-1)$-dimensional face. In contrast, cycle percolation demands the existence of infinite $d$-cycles, thereby generalizing the lattice notion of plaquette percolation. We discuss the sharp phase transition for face percolation and derive comparison results between the critical intensities for face and cycle percolation. Finally, we consider an alternate version of simplex percolation, by declaring simplices to be neighbors whenever they are sufficiently close to each other, and prove a strict inequality involving the critical intensity of this alternate version and that of face percolation.
