Wigner surmises and the two-dimensional Poisson-Voronoi tessellation

Consider the set of points defined by the intersection of a one-dimensional (random) line and a Voronoi tessellation generated by a two-dimensional homogeneous Poisson point process. We show that the nearest-neighbor and higher-order spacing statistics between this set of points and the Poisson points that were used to generate the Voronoi tessellation are given by the Wigner surmises of random matrix theory (with even-integer values of the level-repulsion parameter), when appropriate normalizations are implemented.