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2 results

  • A Duality for Poisson Flats

  • Part of
  • Rolf Schneider
  • Journal:
    Advances in Applied Probability / Volume 31 / Issue 1 / March 1999
    Published online by Cambridge University Press:
    01 July 2016, pp. 63-68
    Print publication:
    March 1999

  • In keeping with the intersection density of a stationary Poisson process of r-flats in Euclidean d-space, where r ≥ d/2, we introduce a notion of closeness, called proximity, for such processes if r < d/2. It is shown that the two notions are connected by a duality: the proximity of a stationary Poisson r-flat process is, up to a constant factor, the intersection density of a certain unique stationary Poisson (d − r)-flat process.