Expected invariants of simplicial complexes obtained from random point samples

This repository contains the source code concerning the paper "Expected invariants of simplicial complexes obtained from random point samples".

Abstract

In this paper, we study the expectation values of topological invariants of the Vietoris–Rips complex and Čech complex for a finite set of sample points on a Riemannian manifold. We show that the Betti number and Euler characteristic of the complexes are Lipschitz functions of the scale parameter and that there is an interval such that the Betti curve converges to the Betti number of the underlying manifold.

Reference

Paik, T., & van Koert, O. (2023). Expected invariants of simplicial complexes obtained from random point samples. Archiv der Mathematik, 1-13.

@article{paik2023expected,
  title={Expected invariants of simplicial complexes obtained from random point samples},
  author={Paik, Taejin and van Koert, Otto},
  journal={Archiv der Mathematik},
  pages={1--13},
  year={2023},
  publisher={Springer}
}

License

This repository is licensed under the MIT License.