  In this paper we introduce a new model of random simplicial complexes
depending on multiple probability parameters. This model includes the
well-known Linial - Meshulam random simplicial complexes and random clique
complexes as special cases. Topological and geometric properties of a
multi-parameter random simplicial complex depend on the whole combination of
the probability parameters and the thresholds for topological properties are
convex sets rather than numbers (as in all previously known models). We discuss
the containment properties, density domains and dimension of the random
simplicial complexes.

Algebraic Topology