Quasi-periodic structures in the large-scale galaxy distribution and three-dimensional Voronoi tessellation

It has been suggested that the void and wall structure associated with the large-scale galaxy distribution might be qualitatively, or perhaps even physically, modeled by a Voronoi tessellation, and that such structure might account for the surprisingly regular, sharp peaks in the galaxy redshift distributions obtained from 'pencil beam' surveys. Taking cell wall crossings by random line segments to correspond to such redshift peaks, an exact expression is derived for the distribution of spacings of these intersections in a three-dimensional Voronoi tessellation. This result verifies that the spacings are nonrandom and quasi-periodic, qualitatively resembling the observed pattern, even though the cell wall structure is generated from randomly placed seeds. Finally, moments of the spacing distribution are used to show that apparently periodic samples, similar to those recently reported, represent only one to two sigma fluctuations in a Voronoi tesselation.