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

There is empirical evidence that the two-point correlation function of the galaxy distribution follows, for small scales, reasonably well a power-law expression xi(r) proportional to r(-gamma) with gamma between 1.5 and 1.9. Nevertheless, most of the point field models suggested in the literature do not have this property. This paper presents a new class of models, which is produced by modifying point fields commonly used in cosmology to mimic the galaxy distribution, but where gamma = 2 is too large. The points are independently and randomly shifted, leading to the desired reduction of the value of gamma.