On the topology of random complexes built over stationary point processes.

@article{Yogeshwaran2015OnTT,
  title={On the topology of random complexes built over stationary point processes.},
  author={D. Yogeshwaran and Robert J. Adler},
  journal={Annals of Applied Probability},
  year={2015},
  volume={25},
  pages={3338-3380}
}
Cech and Vietoris-Rips complexes. In particular, we obtain results about homology, as measured via the growth of Betti numbers, when the vertices are the points of a general stationary point process. This significantly extends earlier results in which the points were either iid observations or the points of a Poisson process. In dealing with general point processes, in which the points exhibit dependence such as attraction, or repulsion, we find phenomena quantitatively different from those… 

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