  High-order structures have been recognised as suitable models for systems
going beyond the binary relationships for which graph models are appropriate.
Despite their importance and surge in research on these structures, their
random cases have been only recently become subjects of interest. One of these
high-order structures is the oriented hypergraph, which relates couples of
subsets of an arbitrary number of vertices. Here we develop the
Erd\H{o}s-R\'enyi model for oriented hypergraphs, which corresponds to the
random realisation of oriented hyperedges of the complete oriented hypergraph.
A particular feature of random oriented hypergraphs is that the ratio between
their expected number of oriented hyperedges and their expected degree or size
is 3/2 for large number of vertices. We highlight the suitability of oriented
hypergraphs for modelling large collections of chemical reactions and the
importance of random oriented hypergraphs to analyse the unfolding of
chemistry.
