Cells of Voronoi diagrams in two dimensions are usually considered as having
edges of zero width. However, this is not the case in several experimental
situations in which the thickness of the edges of the cells is relatively
large. In this paper, the concept of a thick Voronoi tessellation, that is with
edges of non-zero width, is introduced and the the statistics of cell areas, as
thickness changes, are analyzed.Comment: 14 pages, 9 figure