On the statistics of area size in two-dimensional thick Voronoi Diagrams
  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. 
L. Zaninetti
cond-mat.stat-mech