A distributed Voronoi model in the plane

Starting from the classical planar Voronoi tesselation for a stationary Poisson point process a model with random disturbance is introduced. While the Voronoi tesselation can be constructed with the perpendicular lines through the centres of the segments linking any pair of points of the generating point process the authors consider random translations (out of these centres) of the perpendicular lines. The cell to a point is then constructed as the intersection of the half-planes (defined by the perpendicular lines) containing this point-as it is done for the classical Voronoi model. Thus a stationary process of convex nonoverlapping polygons is obtained. For the typical polygon the authors prove formulae for mean area, perimeter and edge number.