  Higher order interactions are increasingly recognised as a fundamental aspect
of complex systems ranging from the brain to social contact networks.
Hypergraph as well as simplicial complexes capture the higher-order
interactions of complex systems and allow to investigate the relation between
their higher-order structure and their function. Here we establish a general
framework for assessing hypergraph robustness and we characterize the critical
properties of simple and higher-order percolation processes. This general
framework builds on the formulation of the random multiplex hypergraph ensemble
where each layer is characterized by hyperedges of given cardinality. We reveal
the relation between higher-order percolation processes in random multiplex
hypergraphs, interdependent percolation of multiplex networks and K-core
percolation. The structural correlations of the random multiplex hypergraphs
are shown to have a significant effect on their percolation properties. The
wide range of critical behaviors observed for higher-order percolation
processes on multiplex hypergraphs elucidates the mechanisms responsible for
the emergence of discontinuous transition and uncovers interesting critical
properties which can be applied to the study of epidemic spreading and
contagion processes on higher-order networks.
