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 corresponding lattice field theory. We study the resulting lattice field theory using the Witten laplacian formulation. We obtain the asymptotics for the directional Lyapunov exponents.
@article{JEDP_1999____A18_0, author = {Wang, Wei-Min}, title = {Supersymmetry, Witten complex and asymptotics for directional Lyapunov exponents in $\mathbf {Z}^d$}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, year = {1999}, pages = {1-16}, zbl = {01810591}, language = {en}, url = {http://dml.mathdoc.fr/item/JEDP_1999____A18_0} }
Wang, Wei-Min. Supersymmetry, Witten complex and asymptotics for directional Lyapunov exponents in $\mathbf {Z}^d$. Journées équations aux dérivées partielles, (1999), pp. 1-16. http://gdmltest.u-ga.fr/item/JEDP_1999____A18_0/
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