2-D Brownian motion in a system of traps: Application of conformal transformations

Abstract

We study two-dimensional Brownian motion in a periodic system of traps using conformal transformations. The system is periodic in the x and y directions. We calculate the ratio of the drift along the y-axis to the drift along the x-axis. The drift of the Brownian particle is induced by conditioning and by the asymmetry of the system of traps. Finally we find the placement of traps which gives the maximal drift ratio.