Operators on random hypergraphs and random simplicial complexes

Random hypergraphs and random simplicial complexes have potential applications in computer science and engineering. Various models of random hypergraphs and random simplicial complexes on n-points have been studied. 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 operators on the space of probability functions on sub-hypergraphs of L. We study the compositions of these operators as well as their actions on the space of probability functions. As applications in computer science, we give algorithms generating large sparse random hypergraphs and large sparse random simplicial complexes.Comment: 22 page

Coboundary expanders

We describe a natural topological generalization of edge expansion for graphs to regular CW complexes and prove that this property holds with high probability for certain random complexes.Comment: Version 2: significant rewrite. 18 pages, title changed, and main theorem extended to more general random complexe