Abstract
We investigate the free energy of nearest-neighbor random walks on ℤd, endowed with a drift along the first axis and evolving in a nonnegative random potential given by i.i.d. random variables. Our main result concerns the ballistic regime in dimensions d≥4, at which we show that quenched and annealed Lyapunov exponents are equal as soon as the strength of the potential is small enough.
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