Intrinsic Volumes of Random Cubical Complexes
Abstract
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 for these intrinsic volumes. For our primary model, we also prove an interleaving theorem for the zeros of the expectedvalue polynomials. The intrinsic volumes of cubical complexes are useful for understanding the shape of random $d$dimensional sets and for characterizing noise in applications.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.5367
 Bibcode:
 2014arXiv1402.5367W
 Keywords:

 Mathematics  Probability;
 60D05;
 52C99
 EPrint:
 17 pages with 7 figures