1 research outputs found
Distance from the Nucleus to a Uniformly Random Point in the 0-cell and the Typical Cell of the Poisson-Voronoi Tessellation
Consider the distances and from the nucleus to a
uniformly random point in the 0-cell and the typical cell, respectively, of the
-dimensional Poisson-Voronoi (PV) tessellation. The main objective of this
paper is to characterize the exact distributions of and .
First, using the well-known relationship between the 0-cell and the typical
cell, we show that the random variable is equivalent in
distribution to the contact distance of the Poisson point process. Next, we
derive a multi-integral expression for the exact distribution of .
Further, we derive a closed-form approximate expression for the distribution of
, which is the contact distribution with a mean corrected by a factor
equal to the ratio of the mean volumes of the 0-cell and the typical cell. An
additional outcome of our analysis is a direct proof of the well-known
spherical property of the PV cells having a large inball