# Maximally Persistent Cycles in Random Geometric Complexes

@article{Bobrowski2015MaximallyPC,
title={Maximally Persistent Cycles in Random Geometric Complexes},
author={O. Bobrowski and M. Kahle and P. Skraba},
journal={arXiv: Probability},
year={2015}
}
• Published 2015
• Mathematics
• arXiv: Probability
• We initiate the study of persistent homology of random geometric simplicial complexes. Our main interest is in maximally persistent cycles of degree-$k$ in persistent homology, for a either the \cech or the Vietoris--Rips filtration built on a uniform Poisson process of intensity $n$ in the unit cube $[0,1]^d$. This is a natural way of measuring the largest "$k$-dimensional hole" in a random point set. This problem is in the intersection of geometric probability and algebraic topology, and is… CONTINUE READING
48 Citations

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