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 exist a long range correlation between the two particles, of $1/r^2$ type. 
Shin-ichi Sasa