Tracer-field cross-correlations with <i>k</i>-nearest neighbour distributions

ABSTRACT In astronomy and cosmology significant effort is devoted to characterizing understanding spatial cross-correlations between points – e.g galaxy positions, high energy neutrino arrival directions, X-ray AGN sources, continuous fields e.g. weak lensing meiand Cosmic Microwave Background maps. Recently, we introduced the k-nearest neighbour (kNN) formalism better characterize clustering of discrete (point) data sets. Here, extend it point field analysis. It combines kNN measurements set with smoothed at many scales. The resulting statistics are sensitive all orders in joint field. We demonstrate that this approach, unlike 2-pt cross-correlation, can measure statistical dependence two sets even when there no linear (Gaussian) correlations them. further framework far more effective than function detecting contaminated by levels noise. For a particularly level noise, cross-correlation haloes underlying matter cosmological simulation, 10 h−1 Mpc 30 Mpc, detected &amp;gt;5σ significance using technique presented here, two-point ∼1σ. Finally, show be well modelled on quasi-linear scales Hybrid Effective Field Theory (HEFT) framework, same bias parameters as used for cross-correlations. substantial improvement power method makes promising tool various applications.