几何约束下构形模型中的巨型构件
Giant component in the configuration model under geometric constraints
摘要：
我们研究了一个巨大的组件的出现在配置模型受到额外的约束的边缘。我们分区的$d$维环面到一个立方晶格含有顶点的车厢的发散数量，只允许局部边缘内部和相邻车厢之间。我们表明，当每隔室的顶点数增长足够快，一个巨大的组件出现在类似的条件下，为标准配置模型。相反，当房室大小固定时，即使标准配置模型有一个巨大的组件，我们的模型也可能没有。局部地，我们的模型类似于配置模型，而在全球范围内，它的属性更类似于一个$d$维晶格。尽管如此，该模型仍然分析易于使用的多类型分支过程与无限数量的类型，并开辟了新的潜在途径来研究渗流的图形与几何性质。
英文摘要：
We study the emergence of a giant component in the configuration model subject to additional constraints on the edges. We partition a $d$-dimensional torus into a cubic lattice with a diverging number of compartments containing vertices and allow only local edges inside and between neighbouring compartments. We show that, when the number of vertices per compartment grows quickly enough, a giant component emerges under similar conditions as for the standard configuration model. Conversely, when the compartment sizes are fixed, our model might not feature a giant component even if the standard configuration model does have one. Locally, our model resembles the configuration model, while globally, it has properties more akin to a $d$-dimensional lattice. Nonetheless the model remains analytically tractable using multitype branching processes with infinite number of types and opens new potential ways to study percolation in graphs with geometric properties.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
