  Many complex systems that exhibit temporal non-pairwise interactions can be
represented by means of generative higher-order network models. Here, we
propose a hidden variables formalism to analytically characterize a general
class of higher-order network models We apply our framework to a temporal
higher-order activity-driven model, providing analytical expressions for the
main topological properties of the time-integrated hypergraphs, depending on
the integration time and the activity distributions characterizing the model.
Furthermore, we provide analytical estimates for the percolation times of
general classes of uncorrelated and correlated hypergraphs. Finally, we
quantify the extent to which the percolation time of empirical social
interactions is underestimated when their higher-order nature is neglected.
