Cosmological cross-correlations and nearest neighbor distributions
  Cross-correlations between datasets are used in many different contexts in
cosmological analyses. Recently, $k$-Nearest Neighbor Cumulative Distribution
Functions ($k{\rm NN}$-${\rm CDF}$) were shown to be sensitive probes of
cosmological (auto) clustering. In this paper, we extend the framework of
nearest neighbor measurements to describe joint distributions of, and
correlations between, two datasets. We describe the measurement of joint $k{\rm
NN}$-${\rm CDF}$s, and show that these measurements are sensitive to all
possible connected $N$-point functions that can be defined in terms of the two
datasets. We describe how the cross-correlations can be isolated by combining
measurements of the joint $k{\rm NN}$-${\rm CDF}$s and those measured from
individual datasets. We demonstrate the application of these measurements in
the context of Gaussian density fields, as well as for fully nonlinear
cosmological datasets. Using a Fisher analysis, we show that measurements of
the halo-matter cross-correlations, as measured through nearest neighbor
measurements are more sensitive to the underlying cosmological parameters,
compared to traditional two-point cross-correlation measurements over the same
range of scales. Finally, we demonstrate how the nearest neighbor
cross-correlations can robustly detect cross correlations between sparse
samples -- the same regime where the two-point cross-correlation measurements
are dominated by noise.
