A New Method for Calculating Counts in Cells

Abstract

In the near future a new generation of CCD based galaxy surveys will enable high precision determination of the N-point correlation functions. The resulting information will help to resolve the ambiguities associated with two-point correlation functions thus constraining theories of structure formation, biasing, and Gaussianity of initial conditions independently of the value of $Ω$. As one the most successful methods to extract the amplitude of higher order correlations is based on measuring the distribution of counts in cells, this work presents an advanced way of measuring it with unprecedented accuracy. Szapudi and Colombi (1996, hereafter \cite{sc96}) identified the main sources of theoretical errors in extracting counts in cells from galaxy catalogs. One of these sources, termed as measurement error, stems from the fact that conventional methods use a finite number of sampling cells to estimate counts in cells. This effect can be circumvented by using an infinite number of cells. This paper presents an algorithm, which, in practice achieves this goal, i.e. it is equivalent to throwing an infinite number of sampling cells in finite time. The errors associated with sampling cells are completely eliminated by this procedure which will be essential for the accurate analysis of future surveys.