Long range spatial correlation between two Brownian particles under external driving

We study the large distance behavior of a steady distribution of two Brownian particles under external driving in a two-dimensional space. Employing a method of perturbative system reduction, we analyze a Fokker–Planck equation that describes the time evolution of the probability density for the two particles. The expression we obtain shows that there exists a long range correlation between the two particles, of 1 / r 2 type.