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

By D. Yogeshwaran, Robert J. Adler. 2012

70 citations recorded by the source corpus.

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 observed in the iid and Poisson cases. From the point of view of topological data analysis, our results seriously impact on considerations of model (non) robustness for statistical inference.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5be7b73187cd69ada6bded9d85250a9e79e3f968

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Maximally Persistent Cycles in Random Geometric Complexes (2015, background): “Similar questions for more general point processes have also been considered in [50].”
Random geometric complexes in the thermodynamic regime (2014, background): “tisfying mild regularity properties. Shortly afterwards, more sophisticated distributional results were proven in [21]. An extension to more general stationary point processes Φ on Rd can be found in [42], while, in the Poisson and binomial settings, [3] looks at these problems from the point of vie”