  Let $L$ be a simplicial complex. In this paper, we study random
sub-hypergraphs and random sub-complexes of $L$. By considering the minimal
complex that a sub-hypergraph can be embedded in and the maximal complex that
can be embedded in a sub-hypergraph, we define some maps on the space of
probability functions on sub-hypergraphs of $L$. We study the compositions of
these maps as well as their actions on the space of probability functions.
