  In this paper, we introduce a novel model for random hypergraphs based on
weighted random connection models. In accordance with the standard theory for
hypergraphs, this model is constructed from a bipartite graph. In our
stochastic model, both vertex sets of this bipartite graph form marked Poisson
point processes and the connection radius is inversely proportional to a
product of suitable powers of the marks. Hence, our model is a common
generalization of weighted random connection models and AB random geometric
graphs. For this hypergraph model, we investigate the limit theory of a variety
of graph-theoretic and topological characteristics such as higher-order degree
distribution, Betti numbers of the associated Dowker complex as well as simplex
counts. In particular, for the latter quantity we identify regimes of
convergence to normal and to stable distribution depending on the
heavy-tailedness of the weight distribution. We conclude our investigation by a
simulation study and an application to the collaboration network extracted from
the arXiv dataset.
