2002/06/20 by Rien van de Weygaert, van de Weygaert, Rien
Economics, Econometrics and Finance · Environmental Science · Physics and Astronomy · #Astrophysics (astro-ph) #FOS: Physical sciences #Impact of Light on Environment and Health #Land Use and Ecosystem Services #Spatial and Panel Data Analysis #astro-ph
paper · pdf · doi:10.48550/arxiv.astro-ph/0206366
Invited contribution to ``Statistical Challenges in Modern Astronomy III'', State College, Pennsylvania, July 2001, eds. G.J. Babu & E.D. Feigelson, Springer-Verlag. 20 pages, 8 figures
arxiv created 2002/06/20 · openalex publication_date 2002/06/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We stress the importance of stochastic geometry as a branch of mathematical\nstatistics particularly suited to model and investigate nontrivial spatial\npatterns. One of its key concepts, Voronoi tessellations, represents a\nversatile and flexible mathematical model for foamlike patterns. Based on a\nseemingly simple definition, Voronoi tessellations define a wealthy stochastic\nnetwork of interconnected anisotropic components, each of which can be\nidentified with the various structural elements of the cosmic galaxy\ndistribution. Here we describe results of an ongoing investigation of a variety\nof aspects of cosmologically relevant spatial distributions and statistics\nwithin the framework of Voronoi tessellations. Interesting is the recent\nfinding of a profound scaling of both clustering strength and clustering extent\nfor the distribution of tessellation nodes, representing galaxy clusters. It\nsuggests a hitherto unexpected fundamental and profound property of foamlike\ngeometries. In a sense, cellular networks may be the source of an intrinsic\n``geometrically biased'' clustering.\n