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

Maps on random hypergraphs and random simplicial complexes