Title: Multi-parameter random simplicial complexes
Abstract: I will describe a model of random simplicial complexes depending on a set of probability parameters, one for each dimension. This model includes many well-known probabilistic models of random simplicial complexes as special cases. Geometric and topological properties of random simplicial complexes specify domains of the multi-parameter space and “thresholds” are boundaries of these domains. In the talk I will describe behavior of the Betti numbers and fundamental groups of simplicial complexes in this model.
The talk is based on a series of joint papers with A. Costa.