Wei-Min Wang Supersymmetry, Witten Complex and Asymptotics for Directional Lyapunov Exponents in $\Z^d$ (371K, .dvi) ABSTRACT. By using a supersymmetric Gaussian representation, we transform the averaged Green's function for random walks in random potentials into a 2-point correlation function of a correponding lattice field theory. We study the resulting lattice field theory using the Witten Laplacian formulation. We obtain the asymptotics for the directional Lyapunov exponents.