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Supersymmetry, Witten complex and asymptotics for directional Lyapunov exponents in 𝐙 d

Wei-Min Wang — 1999

Journées équations aux dérivées partielles

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.

Fonction de Correlation pour des Mesures Complexes

Wei Min Wang

Séminaire Équations aux dérivées partielles

We study a class of holomorphic complex measures, which are close in an appropriate sense to a complex Gaussian. We show that these measures can be reduced to a product measure of real Gaussians with the aid of a maximum principle in the complex domain. The formulation of this problem has its origin in the study of a certain class of random Schrödinger operators, for which we show that the expectation value of the Green’s function decays exponentially.

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