2006/11/01 by Konstantin Borovkov, K. A. Borovkov, Borovkov, K. A. +2
Environmental Science · Mathematics · #60J20 #60K35 #65C99 #FOS: Mathematics #Morphological variations and asymmetry #Point processes and geometric inequalities #Probability (math.PR) #Soil Geostatistics and Mapping #math.PR #msc:60J20 #msc:60K35 #msc:65C99
paper · pdf · doi:10.48550/arxiv.math/0611031
11 pages, 10 figures
arxiv created 2006/11/01 · openalex publication_date 2006/11/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a new class of dynamic point process models with simple and intuitive dynamics that are based on the Voronoi tessellations generated by the processes. Under broad conditions, these processes prove to be ergodic and produce, on stabilisation, a wide range of clustering patterns. In the paper, we present results of simulation studies of three statistical measures (Thiel's redundancy, van Lieshout and Baddeley's J-function and the empirical distribution of the Voronoi nearest neighbours' numbers) for inference on these models from the clustering behaviour in the stationary regime. In particular, we make comparisons with the area-interaction processes of Baddeley and van Lieshout.