2017/03/11 by Iván Marín, Marin, Ivan
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Advanced Algebra and Geometry #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1703.03987
We introduce a new `geometric realization' of an (abstract) simplicial complex, inspired by probability theory. This space (and its completion) is a metric space, which has the right (weak) homotopy type, and which can be compared with the usual geometric realization through a natural map, which has probabilistic meaning : it associates to a random variable its probability mass function. This `probability map' function is proved to be a (Serre) fibration and a (weak) homotopy equivalence.