Point field models for the galaxy point pattern : Modelling the singularity of the two-point correlation function

Abstract
There is empirical evidence that the two-point correlation function of the galaxy distribution follows, for small scales, reasonably well a power-law expression ξ(r) / αr^−γ with γ between 1.5 and 1.9. Nevertheless, most of the point eld models suggested in the literature do not have this property. This paper presents a new class of models, which is produced by modifying point elds commonly used in cosmology to mimic the galaxy distribution, but where γ = 2 is too large. The points are independently and randomly shifted, leading to the desired reduction of the value of γ.
Description
Bibliographic reference
SNETHLAGE, M. ; Martinez Garcia, Vicente ; Stoyan, D. ; Saar, E., 2002, Point field models for the galaxy point pattern : Modelling the singularity of the two-point correlation function, Astronomy and Astrophysics, vol. 388, no. 3, p. 758-765