Conditional cumulants in a weakly non-linear regime

Abstract

We introduce conditional cumulants as a set of unique statistics closely related to N-point correlation functions and to cumulants of moments of counts in cells. We show that they can be viewed in three equivalent ways: (i) as particular integrals of the N-point correlation functions, (ii) as integrated monopole moments of the bispectrum, and (iii) as statistics associated with neighbour counts. As monopole statistics, they carry similar information to the cumulants SN, the most widely spread higher-order statistics usually measured from counts in cells. While it has been proved that counts in cells can only be approximately corrected for edge effects, we show that well-tested, edge-corrected estimators can be successfully adapted for conditional cumulants. Since edge-effect errors typically dominate large scales, it is expected that it will be possible to measure conditional cumulants with higher accuracy in the interesting large-scale regime. To lay the theoretical ground work for future applications, we compute the predictions of weakly non-linear perturbation theory for conditional cumulants. We demonstrate the use of edge-corrected estimators in a set of simulations and measure conditional cumulants, and compare the results with our theoretical predictions in real and redshift space. We find excellent agreement, especially on scales 20 h −1 Mpc. Owing to their advantageous statistical