Intrinsic Volumes of Random Cubical Complexes

@article{Werman2016IntrinsicVO,
  title={Intrinsic Volumes of Random Cubical Complexes},
  author={M. Werman and Matthew L. Wright},
  journal={Discrete & Computational Geometry},
  year={2016},
  volume={56},
  pages={93-113}
}
  • M. Werman, Matthew L. Wright
  • Published 2016
  • Mathematics, Computer Science
  • Discrete & Computational Geometry
  • Intrinsic volumes, which generalize both Euler characteristic and Lebesgue volume, are important properties of d-dimensional sets. A random cubical complex is a union of unit cubes, each with vertices on a regular cubic lattice, constructed according to some probability model. We analyze and give exact polynomial formulae, dependent on a probability, for the expected value and variance of the intrinsic volumes of several models of random cubical complexes. We then prove a central limit theorem… CONTINUE READING
    9 Citations

    Figures, Tables, and Topics from this paper.

    Homotopy Types of Random Cubical Complexes
    • 2
    • PDF
    Multivariate central limit theorems for Rademacher functionals with applications
    • 9
    • Highly Influenced
    • PDF
    Percolation on Homology Generators in Codimension One
    • 1
    • PDF
    Limit Theorems for Random Cubical Homology
    • 9
    • Highly Influenced
    • PDF
    Betti Numbers of Gaussian Excursions in the Sparse Regime

    References

    SHOWING 1-10 OF 30 REFERENCES
    Limit theorems for Betti numbers of random simplicial complexes
    • 93
    • PDF
    Random Geometric Complexes
    • M. Kahle
    • Computer Science, Mathematics
    • Discret. Comput. Geom.
    • 2011
    • 120
    • PDF
    Topology of Random 2-Complexes
    • 47
    • PDF
    Algorithms for the computation of the Minkowski functionals of deterministic and random polyconvex sets
    • 28
    • PDF
    Homological connectivity of random k-dimensional complexes
    • 121
    • PDF
    Local Properties of Binary Images in Two Dimensions
    • S. B. Gray
    • Computer Science
    • IEEE Transactions on Computers
    • 1971
    • 285
    Introduction to Geometric Probability
    • 368
    • PDF
    Hadwiger Integration of Random Fields
    • 1
    • PDF
    Stochastic and Integral Geometry
    • 524
    Plaquettes, Spheres, and Entanglement
    • 22
    • PDF