Wei-Min Wang Supersymmetry, Witten complex and Asymptotics for Directional Lyapunov Exponents in $Z^d$ (369K, dvi file) ABSTRACT. We study the long distance asymptotics for random walks in random potentials using the analytical formulation. Via the supersymmetric representation, the problem is reduced to the study of certain Witten Laplcians. We obtain the asymptotics for the directional Lyapunov exponents.