2001/02/28 by M. Kerscher
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Bayesian Methods and Mixture Models #Correlation function (quantum field theory) #Diffusion and Search Dynamics #Distribution (mathematics) #Function (biology) #Gauss #Gaussian #Gaussian process #Gaussian random field #Mathematical analysis #Mathematics #Physics #Point process #Point processes and geometric inequalities #Poisson distribution #Quantum mechanics #Random field #Statistical physics #Statistics #astro-ph #cond-mat.stat-mech #math.PR #physics.data-an
paper · pdf · doi:10.1103/physreve.64.056109
published as Phys. Rev. E, 64 (2001) 056109 · 19 pages, 4 figures, PRE in press, now including comments on hierarchical models and a comparison of random fields vs. random point sets
arxiv created 2001/08/07 · openalex publication_date 2001/10/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The definition and the properties of a Gaussian point distribution, in contrast to the well-known properties of a Gaussian random field are discussed. Constraints for the number density and the two-point correlation function arise. A simple method for the simulation of this so-called Gauss-Poisson point process is given and illustrated with an example. A comparison of the distribution of galaxies in the PSCz catalog with the Gauss-Poisson process underlines the importance of higher-order correlation functions for the description for the galaxy distribution. The construction of the Gauss-Poisson point process is extended to the n-point Poisson cluster process, now incorporating correlation functions up to nth order. Simulation methods and constraints on the correlation functions are discussed for an n-point case and detailed for a three-point case. As another approach, well suited for strongly clustered systems, the generalized halo model is discussed. The influence of substructure inside the halos on the two- and three-point correlation functions is calculated in this model.