Maximally Persistent Cycles in Random Geometric Complexes

  title={Maximally Persistent Cycles in Random Geometric Complexes},
  author={O. Bobrowski and M. Kahle and P. Skraba},
  journal={arXiv: Probability},
  • O. Bobrowski, M. Kahle, P. Skraba
  • 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
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