Simplicial Random Variables
Algebraic Topology
2020-09-29 v3 Probability
Abstract
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.
Cite
@article{arxiv.1703.03987,
title = {Simplicial Random Variables},
author = {Ivan Marin},
journal= {arXiv preprint arXiv:1703.03987},
year = {2020}
}