Cumulant Correlators in 2D and 3D Scale Free Simulations
  Shape dependence of higher order correlations introduces complication in direct determination of these quantities. For this reason theoretical and observational progress has been restricted in calculating one point distribution functions and related moments. Methods based on factorial moments of two point count probability distribution (cumulant correlators) were recently shown to be efficient in subtracting discreteness effects and extracting useful information from galaxy catalogs. We use these cumulant correlators $Q_{NM}$ to study clustering in scale free simulations both in two and three dimensions. Using this method in the highly nonlinear regime we were able to separate hierarchal amplitudes $Q_3, R_a and R_b$ associated with different tree graphs contributing to third and fourth order correlation functions. They were found to increase with power on large scales. Results based on factorial moments of one point cumulants show very good agreement with that on cumulant correlators. Comparison of simulation results with perturbation theory and extended perturbation theory were found to be in reasonable agreement. Comparisons were also made against predictions from hierarchal models for higher order correlations. We argue that finite volume corrections are very important for computation of cumulant correlators. 
Dipak Munshi and Adrian L. Melott