In this seminar we present a model of random simplicial complexes, which are a multi-dimensional generalization of the Erdős-Rényi model of random graphs. The focus of the article is on the combinatorial properties of large random simplicial complexes. In particular, we explore under which conditions a random simplicial complex contains a given simplicial complex. We introduce the concept of balanced abstract simplicial complexes and use basic theory of simplicial complexes to construct some examples. The properties of balanced simplicial complexes enable us to further examine the dimension of large random simplicial complexes.
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