Lyapunov exponents of random walks in small random potential: the upper bound

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We consider the simple random walk on Zᵈ evolving in a random i.i.d. potential taking values in [0,+∞). The potential is not assumed integrable, and can be rescaled by a multiplicative factor λ> 0. Completing the work started in a companion paper, we give the asymptotic behaviour of the Lyapunov exponents for d ≥ 3, both annealed and quenched, as the scale parameter λ tends to zero.