  When two populations of "particles" move in opposite directions, like
oppositely charged colloids under an electric field or intersecting flows of
pedestrians, they can move collectively, forming lanes along their direction of
motion. The nature of this "laning transition" is still being debated and, in
particular, the pair correlation functions, which are the key observables to
quantify this phenomenon, have not been characterized yet. Here, we determine
the correlations using an analytical approach based on a linearization of the
stochastic equations for the density fields, which is valid for dense systems
of soft particles. We find that the correlations decay algebraically along the
direction of motion, and have a self-similar exponential profile in the
transverse direction. Brownian dynamics simulations confirm our theoretical
predictions and show that they also hold beyond the validity range of our
analytical approach, pointing to a universal behavior.
