Title: Aggregation models on hypergraphs Show Chinese title

Title: 超图上的聚合模型

Abstract: Following a newly introduced approach by Rasetti and Merelli we investigate the possibility to extract topological information about the space where interacting systems are modelled. From the statistical datum of their observable quantities, like the correlation functions, we show how to reconstruct the activities of their constitutive parts which embed the topological information. The procedure is implemented on a class of polymer models on hypergraphs with hard-core interactions. We show that the model fulfils a set of iterative relations for the partition function that generalise those introduced by Heilmann and Lieb for the monomer-dimer case. After translating those relations into structural identities for the correlation functions we use them to test the precision and the robustness of the inverse problem. Finally the possible presence of a further interaction of peer-to-peer type is considered and a criterion to discover it is identified. Show Chinese abstract

Abstract: 借鉴Rasetti和Merelli提出的新方法，我们研究了从相互作用系统的可观测量（例如关联函数）的统计数据中提取空间拓扑信息的可能性。 我们展示了如何通过这些可观测量重构构成部分的活动，这些活动嵌入了拓扑信息。 该过程在一个具有硬核相互作用的超图聚合物模型类上实现。 我们证明该模型满足广义Heilmann和Lieb为单体-二聚体情况引入的一组分区函数迭代关系。 将这些关系转化为关联函数的结构恒等式后，我们用它们来检验逆问题的精度和鲁棒性。 最后，考虑了可能存在的一种额外的点对点相互作用，并确定了一种识别它的标准。