Constructing, characterizing, and simulating Gaussian and higher-order point distributions
Abstract
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. The comparison of the distribution of galaxies in the PSCz catalogue 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 the nth-order. The simulation methods and constraints on the correlation functions are discussed for the n-point case and detailed for the 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.
Cite
@article{arxiv.astro-ph/0102153,
title = {Constructing, characterizing, and simulating Gaussian and higher-order point distributions},
author = {M. Kerscher},
journal= {arXiv preprint arXiv:astro-ph/0102153},
year = {2009}
}
Comments
19 pages, 4 figures, PRE in press, now including comments on hierarchical models and a comparison of random fields vs. random point sets