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Aggregation models on hypergraphs. (English) Zbl 1364.82071
Summary: 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.

##### MSC:
 82D60 Statistical mechanical studies of polymers 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics 05C90 Applications of graph theory 05C15 Coloring of graphs and hypergraphs
##### Keywords:
polymer model; hypergraphs; inverse problem; complex systems
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