  We consider quenched and annealed Lyapunov exponents for the Green's function
of $-\Delta+\gamma V$, where the potentials $V(x), x\in\Z^d$, are i.i.d.
nonnegative random variables and $\gamma>0$ is a scalar. We present a
probabilistic proof that both Lyapunov exponents scale like $c\sqrt{\gamma}$ as
$\gamma$ tends to 0. Here the constant $c$ is the same for the quenched as for
the annealed exponent and is computed explicitly. This improves results
obtained previously by Wei-Min Wang. We also consider other ways to send the
potential to zero than multiplying it by a small number.
